Haruzo Hida
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198571025
- eISBN:
- 9780191718946
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198571025.001.0001
- Subject:
- Mathematics, Algebra
The 1995 work by Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book ...
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The 1995 work by Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book describes a generalization of their techniques to Hilbert modular forms (towards the proof of the celebrated ‘R=T’ theorem) and applications of the theorem that have been found. Applications include a proof of the torsion of the adjoint Selmer group (over a totally real field F and over the Iwasawa tower of F) and an explicit formula of the L-invariant of the arithmetic p-adic adjoint L-functions. This implies the torsion of the classical anticyclotomic Iwasawa module of a CM field over the Iwasawa algebra. When specialized to an elliptic Tate curve over F by the L-invariant formula, the invariant of the adjoint square of the curve has exactly the same expression as the one in the conjecture of Mazur-Tate-Teitelbaum (which is for the standard L-function of the elliptic curve and is now a theorem of Greenberg-Stevens).Less
The 1995 work by Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book describes a generalization of their techniques to Hilbert modular forms (towards the proof of the celebrated ‘R=T’ theorem) and applications of the theorem that have been found. Applications include a proof of the torsion of the adjoint Selmer group (over a totally real field F and over the Iwasawa tower of F) and an explicit formula of the L-invariant of the arithmetic p-adic adjoint L-functions. This implies the torsion of the classical anticyclotomic Iwasawa module of a CM field over the Iwasawa algebra. When specialized to an elliptic Tate curve over F by the L-invariant formula, the invariant of the adjoint square of the curve has exactly the same expression as the one in the conjecture of Mazur-Tate-Teitelbaum (which is for the standard L-function of the elliptic curve and is now a theorem of Greenberg-Stevens).
S.K. Jain, Ashish K. Srivastava, and Askar A. Tuganbaev
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199664511
- eISBN:
- 9780191746024
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199664511.001.0001
- Subject:
- Mathematics, Algebra
This book provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a ...
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This book provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a homological property. The finiteness conditions and homological properties are closely interrelated in the sense that either hypothesis induces the other in some form. The main objective behind writing this volume is the absence of a book that contains most of the relevant material on the subject. Since before the last half century, numerous authors including Armendariz, Beidar, Camillo, Chatters, Clark, Cohen, Cozzens, Faith, Farkas, Fisher, Goodearl, Gómez Pardo, Guil Asensio, Hajarnavis, Huynh, Jain, Kohler, Levy, López-Permouth, Mohamed, Ornstein, Osofsky, Singh, Skornyakov, Smith, Tuganbaev, and Wisbauer have investigated rings whose factor rings or factor modules have a finiteness condition or a homological property. They made important contributions leading to new directions and questions that have been listed at the end of each chapter for the benefit of future researchers. The bibliography has more than 200 references and is not claimed to be exhaustive.Less
This book provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a homological property. The finiteness conditions and homological properties are closely interrelated in the sense that either hypothesis induces the other in some form. The main objective behind writing this volume is the absence of a book that contains most of the relevant material on the subject. Since before the last half century, numerous authors including Armendariz, Beidar, Camillo, Chatters, Clark, Cohen, Cozzens, Faith, Farkas, Fisher, Goodearl, Gómez Pardo, Guil Asensio, Hajarnavis, Huynh, Jain, Kohler, Levy, López-Permouth, Mohamed, Ornstein, Osofsky, Singh, Skornyakov, Smith, Tuganbaev, and Wisbauer have investigated rings whose factor rings or factor modules have a finiteness condition or a homological property. They made important contributions leading to new directions and questions that have been listed at the end of each chapter for the benefit of future researchers. The bibliography has more than 200 references and is not claimed to be exhaustive.
David P. Blecher and Christian Le Merdy
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198526599
- eISBN:
- 9780191712159
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526599.003.0008
- Subject:
- Mathematics, Pure Mathematics
This chapter has three main goals. First, to examine Hilbert C*-modules (and their W*-algebra variant, W *-modules) as operator modules. It aims to show that the theory of C *-modules fits ...
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This chapter has three main goals. First, to examine Hilbert C*-modules (and their W*-algebra variant, W *-modules) as operator modules. It aims to show that the theory of C *-modules fits comfortably into the operator module framework. Second, to consider space X. In particular, it will discuss the noncommutative Shilov boundary ☐(X) of X. TRO methods and this Shilov boundary provide important insights into the structure of X. Third, to illustrate how C*-module and TRO methods can lead to interesting results about operator spaces. Notes and historical remarks are presented at the end of the chapter.Less
This chapter has three main goals. First, to examine Hilbert C*-modules (and their W*-algebra variant, W *-modules) as operator modules. It aims to show that the theory of C *-modules fits comfortably into the operator module framework. Second, to consider space X. In particular, it will discuss the noncommutative Shilov boundary ☐(X) of X. TRO methods and this Shilov boundary provide important insights into the structure of X. Third, to illustrate how C*-module and TRO methods can lead to interesting results about operator spaces. Notes and historical remarks are presented at the end of the chapter.
David P. Blecher and Christian Le Merdy
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198526599
- eISBN:
- 9780191712159
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526599.003.0003
- Subject:
- Mathematics, Pure Mathematics
This chapter discusses the basics of operator modules. Topics covered include Hilbert modules, operator modules over operator algebras, two module tensor products, module maps, module map extension ...
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This chapter discusses the basics of operator modules. Topics covered include Hilbert modules, operator modules over operator algebras, two module tensor products, module maps, module map extension theorems, function modules, and dual operator modules. Notes and historical remarks are presented at the end of the chapter.Less
This chapter discusses the basics of operator modules. Topics covered include Hilbert modules, operator modules over operator algebras, two module tensor products, module maps, module map extension theorems, function modules, and dual operator modules. Notes and historical remarks are presented at the end of the chapter.
Peter Carruthers
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199207077
- eISBN:
- 9780191708909
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199207077.003.0001
- Subject:
- Philosophy, Philosophy of Mind
This chapter lays out the main arguments supporting massive modularity and explicates the notion of ‘module’ that those arguments support (which is significantly weaker than on Fodor’s influential ...
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This chapter lays out the main arguments supporting massive modularity and explicates the notion of ‘module’ that those arguments support (which is significantly weaker than on Fodor’s influential account). It argues that modularity is a property of biological systems quite generally, and of animal minds in particular. It also defends the viability of evolutionary psychology as a scientific research program. The chapter criticizes Fodor’s argument that encapsulated forms of modularity are a requirement of computational tractability, arguing that the latter can be assured through the use of various kinds of cognitive heuristic.Less
This chapter lays out the main arguments supporting massive modularity and explicates the notion of ‘module’ that those arguments support (which is significantly weaker than on Fodor’s influential account). It argues that modularity is a property of biological systems quite generally, and of animal minds in particular. It also defends the viability of evolutionary psychology as a scientific research program. The chapter criticizes Fodor’s argument that encapsulated forms of modularity are a requirement of computational tractability, arguing that the latter can be assured through the use of various kinds of cognitive heuristic.
Peter Carruthers
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199207077
- eISBN:
- 9780191708909
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199207077.003.0002
- Subject:
- Philosophy, Philosophy of Mind
This chapter argues that the minds of all animals (even honey bees) are organized around a perception/belief/desire/planning/motor-control architecture. There are also multiple modules for generating ...
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This chapter argues that the minds of all animals (even honey bees) are organized around a perception/belief/desire/planning/motor-control architecture. There are also multiple modules for generating beliefs, for generating desires and other forms of motivation, for storing those states in memory, and for controlling action. Evidence of dual visual systems in mammals, and against the existence of any sort of general learning is presented. It is argued that some animals might utilize mental rehearsal of action schemata to increase the flexibility of their decision making.Less
This chapter argues that the minds of all animals (even honey bees) are organized around a perception/belief/desire/planning/motor-control architecture. There are also multiple modules for generating beliefs, for generating desires and other forms of motivation, for storing those states in memory, and for controlling action. Evidence of dual visual systems in mammals, and against the existence of any sort of general learning is presented. It is argued that some animals might utilize mental rehearsal of action schemata to increase the flexibility of their decision making.
Peter Carruthers
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199207077
- eISBN:
- 9780191708909
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199207077.003.0007
- Subject:
- Philosophy, Philosophy of Mind
This chapter provides a modularist account of the main elements of human practical reasoning. It appeals to a norms module that is structured in such a way as to attach intrinsic motivation to stored ...
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This chapter provides a modularist account of the main elements of human practical reasoning. It appeals to a norms module that is structured in such a way as to attach intrinsic motivation to stored normative beliefs, and it suggests that our tendency to express our desires in descriptive form (e.g., as statements of value) enables us to reap the benefits of our theoretical reasoning capacities for practical purposes. It distinguishes between two kinds of practical reasoning and intention (System 1 and System 2), and argues against the view that beliefs alone can motivate action. The chapter closes with discussion and endorsement of Wegner’s thesis that conscious will is an illusion.Less
This chapter provides a modularist account of the main elements of human practical reasoning. It appeals to a norms module that is structured in such a way as to attach intrinsic motivation to stored normative beliefs, and it suggests that our tendency to express our desires in descriptive form (e.g., as statements of value) enables us to reap the benefits of our theoretical reasoning capacities for practical purposes. It distinguishes between two kinds of practical reasoning and intention (System 1 and System 2), and argues against the view that beliefs alone can motivate action. The chapter closes with discussion and endorsement of Wegner’s thesis that conscious will is an illusion.
Dan Sperber
- Published in print:
- 2005
- Published Online:
- January 2007
- ISBN:
- 9780195179675
- eISBN:
- 9780199869794
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195179675.003.0004
- Subject:
- Philosophy, Metaphysics/Epistemology
This chapter addresses the flexibility problem for massive modularity. It argues that massively modular architectures exhibit flexibility largely as a result of context-sensitive competition between ...
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This chapter addresses the flexibility problem for massive modularity. It argues that massively modular architectures exhibit flexibility largely as a result of context-sensitive competition between modules for the allocation of cognitive resources. Thus, it is the cognitive system as a whole that exhibits flexibility, rather than any particular subsystem within it.Less
This chapter addresses the flexibility problem for massive modularity. It argues that massively modular architectures exhibit flexibility largely as a result of context-sensitive competition between modules for the allocation of cognitive resources. Thus, it is the cognitive system as a whole that exhibits flexibility, rather than any particular subsystem within it.
Anna Shusterman and Elizabeth Spelke
- Published in print:
- 2005
- Published Online:
- January 2007
- ISBN:
- 9780195179675
- eISBN:
- 9780199869794
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195179675.003.0006
- Subject:
- Philosophy, Metaphysics/Epistemology
This chapter argues that human and animal minds indeed depend on a collection of domain-specific, task-specific, and encapsulated cognitive systems: on a set of cognitive ‘modules’ in Fodor's sense. ...
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This chapter argues that human and animal minds indeed depend on a collection of domain-specific, task-specific, and encapsulated cognitive systems: on a set of cognitive ‘modules’ in Fodor's sense. It also argues that human and animal minds are endowed with domain-general, central systems that orchestrate the information delivered by core knowledge systems. The chapter begins by reviewing the literature on spatial reorientation in animals and in young children, arguing that spatial reorientation bears the hallmarks of core knowledge and of modularity. It then considers studies of older children and adults, arguing that human spatial representations change qualitatively over development and show capacities not found in any other species. Finally, it presents two new experiments that investigate the role of emerging spatial language in uniquely human navigation performance.Less
This chapter argues that human and animal minds indeed depend on a collection of domain-specific, task-specific, and encapsulated cognitive systems: on a set of cognitive ‘modules’ in Fodor's sense. It also argues that human and animal minds are endowed with domain-general, central systems that orchestrate the information delivered by core knowledge systems. The chapter begins by reviewing the literature on spatial reorientation in animals and in young children, arguing that spatial reorientation bears the hallmarks of core knowledge and of modularity. It then considers studies of older children and adults, arguing that human spatial representations change qualitatively over development and show capacities not found in any other species. Finally, it presents two new experiments that investigate the role of emerging spatial language in uniquely human navigation performance.
Jack C. Lyons
- Published in print:
- 2009
- Published Online:
- January 2009
- ISBN:
- 9780195373578
- eISBN:
- 9780199871988
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195373578.003.0004
- Subject:
- Philosophy, Metaphysics/Epistemology
This chapter articulates and defends the view that a perceptual belief is a belief that is the output of a perceptual system, i.e., a perceptual module, where the notion of a perceptual module is ...
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This chapter articulates and defends the view that a perceptual belief is a belief that is the output of a perceptual system, i.e., a perceptual module, where the notion of a perceptual module is defined in nonepistemic and nonexperiential terms. The concept of a perceptual module, like the more general concept of a cognitive system, is derived from methodological presuppositions of contemporary cognitive neuroscience. The central thesis of this chapter gives us a principled and naturalistic distinction between perceptual beliefs and other beliefs, and, it is argued, it gives us an intuitively correct one. The theory entails that “zombies” and other creatures utterly lacking in perceptual experiences can nonetheless have (justified) perceptual beliefs.Less
This chapter articulates and defends the view that a perceptual belief is a belief that is the output of a perceptual system, i.e., a perceptual module, where the notion of a perceptual module is defined in nonepistemic and nonexperiential terms. The concept of a perceptual module, like the more general concept of a cognitive system, is derived from methodological presuppositions of contemporary cognitive neuroscience. The central thesis of this chapter gives us a principled and naturalistic distinction between perceptual beliefs and other beliefs, and, it is argued, it gives us an intuitively correct one. The theory entails that “zombies” and other creatures utterly lacking in perceptual experiences can nonetheless have (justified) perceptual beliefs.
Kim Sterelny
- Published in print:
- 2007
- Published Online:
- May 2007
- ISBN:
- 9780195310139
- eISBN:
- 9780199871209
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195310139.003.0014
- Subject:
- Philosophy, Philosophy of Mind
This chapter argues that much human decision-making has a high cognitive load, that is, agents make satisfying decisions only by accessing and effectively using information that is hard to get, ...
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This chapter argues that much human decision-making has a high cognitive load, that is, agents make satisfying decisions only by accessing and effectively using information that is hard to get, interpret, or both. When the type of information needed for good decision-making is predictable over evolutionarily significant time frames, there is likely to be a modular explanation of its intelligent use. When the environment is stable in the right way, natural selection can pre-equip agents to register the relevant information and use it efficiently. But human environments are variable, and as a consequence there are many high-cognitive-load problems that we face whose informational requirements are not stable over evolutionary time. This chapter argues that our capacity to respond successfully to these novel problems depends on two other evolved strategies. The first is informational niche construction. Informational engineering is an ancient feature of human lifeways, and it is argued that human minds are adapted to this social transmission of information. The second strategy is less sensitive to the pace of change. Most obviously, we store information in the environment. This too is an ancient feature of human lifeways. Human minds are adapted not just to relatively invariant features of human environments, but also to changeable ones. Adaptive action in the face of novel challenges depends on some combination of informational niche construction and epistemic technology.Less
This chapter argues that much human decision-making has a high cognitive load, that is, agents make satisfying decisions only by accessing and effectively using information that is hard to get, interpret, or both. When the type of information needed for good decision-making is predictable over evolutionarily significant time frames, there is likely to be a modular explanation of its intelligent use. When the environment is stable in the right way, natural selection can pre-equip agents to register the relevant information and use it efficiently. But human environments are variable, and as a consequence there are many high-cognitive-load problems that we face whose informational requirements are not stable over evolutionary time. This chapter argues that our capacity to respond successfully to these novel problems depends on two other evolved strategies. The first is informational niche construction. Informational engineering is an ancient feature of human lifeways, and it is argued that human minds are adapted to this social transmission of information. The second strategy is less sensitive to the pace of change. Most obviously, we store information in the environment. This too is an ancient feature of human lifeways. Human minds are adapted not just to relatively invariant features of human environments, but also to changeable ones. Adaptive action in the face of novel challenges depends on some combination of informational niche construction and epistemic technology.
Scott Atran
- Published in print:
- 2007
- Published Online:
- May 2007
- ISBN:
- 9780195310139
- eISBN:
- 9780199871209
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195310139.003.0018
- Subject:
- Philosophy, Philosophy of Mind
This chapter envisions religion, in general, and awareness of the supernatural, in particular, as a converging by-product of several cognitive and emotional mechanisms that evolved under natural ...
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This chapter envisions religion, in general, and awareness of the supernatural, in particular, as a converging by-product of several cognitive and emotional mechanisms that evolved under natural selection for mundane adaptive tasks. As human beings routinely interact, they naturally tend to exploit these by-products to solve inescapable, existential problems that have no apparent worldly solution, such as the inevitability of death and the ever-present threat of deception by others. Religion involves costly and hard-to-fake commitment to a counterintuitive world of supernatural agents that master such existential anxieties. The greater one's display of costly commitment to that factually absurd world — as in Abraham's willingness to sacrifice his beloved son for nothing palpable save faith in a “voice” demanding the killing — the greater society's trust in that person's ability and will to help out others with their inescapable problems.Less
This chapter envisions religion, in general, and awareness of the supernatural, in particular, as a converging by-product of several cognitive and emotional mechanisms that evolved under natural selection for mundane adaptive tasks. As human beings routinely interact, they naturally tend to exploit these by-products to solve inescapable, existential problems that have no apparent worldly solution, such as the inevitability of death and the ever-present threat of deception by others. Religion involves costly and hard-to-fake commitment to a counterintuitive world of supernatural agents that master such existential anxieties. The greater one's display of costly commitment to that factually absurd world — as in Abraham's willingness to sacrifice his beloved son for nothing palpable save faith in a “voice” demanding the killing — the greater society's trust in that person's ability and will to help out others with their inescapable problems.
A. A. Ivanov
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198527596
- eISBN:
- 9780191713163
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527596.003.0006
- Subject:
- Mathematics, Pure Mathematics
This chapter proves the existence of a completion of the amalgam G which is constrained at level 2. This is achieved by studying the non-trivial representations of G (the representations of the ...
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This chapter proves the existence of a completion of the amalgam G which is constrained at level 2. This is achieved by studying the non-trivial representations of G (the representations of the universal completion group of G) of minimal degree. This degree turns out to be 1333 which is the famous minimal character degree of J4.Less
This chapter proves the existence of a completion of the amalgam G which is constrained at level 2. This is achieved by studying the non-trivial representations of G (the representations of the universal completion group of G) of minimal degree. This degree turns out to be 1333 which is the famous minimal character degree of J4.
Haruzo Hida
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198571025
- eISBN:
- 9780191718946
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198571025.003.0005
- Subject:
- Mathematics, Algebra
This chapter proves the torsion of the anticyclotomic Iwasawa module of a (p-ordinary) CM field, and presents an explicit formula of the L-invariant of the CM field, which is a natural generalization ...
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This chapter proves the torsion of the anticyclotomic Iwasawa module of a (p-ordinary) CM field, and presents an explicit formula of the L-invariant of the CM field, which is a natural generalization of the formula by Ferrero-Greenberg and Gross-Koblitz from the 1970s for imaginary quadratic fields. These results are proven through the comparison theorem (the ‘R=T’ theorem) between the Iwasawa-theoretic version of the universal deformation ring and the universal nearly p-ordinary Hecke algebra over the (infinite) cyclotomic Iwasawa tower. These combined results enable us to compute the adjoint L-invariant of a CM theta family in terms of the U(p)-eigenvalue of the theta family.Less
This chapter proves the torsion of the anticyclotomic Iwasawa module of a (p-ordinary) CM field, and presents an explicit formula of the L-invariant of the CM field, which is a natural generalization of the formula by Ferrero-Greenberg and Gross-Koblitz from the 1970s for imaginary quadratic fields. These results are proven through the comparison theorem (the ‘R=T’ theorem) between the Iwasawa-theoretic version of the universal deformation ring and the universal nearly p-ordinary Hecke algebra over the (infinite) cyclotomic Iwasawa tower. These combined results enable us to compute the adjoint L-invariant of a CM theta family in terms of the U(p)-eigenvalue of the theta family.
David P. Blecher and Christian Le Merdy
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198526599
- eISBN:
- 9780191712159
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198526599.003.0007
- Subject:
- Mathematics, Pure Mathematics
This chapter discusses several interesting criteria which force an operator algebra to be selfadjoint. Such results are in some sense ‘negative’ in nature, showing that certain results or themes ...
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This chapter discusses several interesting criteria which force an operator algebra to be selfadjoint. Such results are in some sense ‘negative’ in nature, showing that certain results or themes which are important for C*-algebras, may not be transferred to general operator algebras, or at least not in a literal way. Topics covered include OS-nuclear maps and the weak expectation property, Hilbert module characterizations, tensor product characterizations, and amenability and virtual diagonals. Notes and historical remarks are presented at the end of the chapter.Less
This chapter discusses several interesting criteria which force an operator algebra to be selfadjoint. Such results are in some sense ‘negative’ in nature, showing that certain results or themes which are important for C*-algebras, may not be transferred to general operator algebras, or at least not in a literal way. Topics covered include OS-nuclear maps and the weak expectation property, Hilbert module characterizations, tensor product characterizations, and amenability and virtual diagonals. Notes and historical remarks are presented at the end of the chapter.
John R. Anderson
- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780195324259
- eISBN:
- 9780199786671
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195324259.001.0001
- Subject:
- Psychology, Cognitive Models and Architectures
This book takes its title from the last lecture by Allen Newell, one of the pioneers of cognitive science. He said, “The question for me is how can the human mind occur in the physical universe? We ...
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This book takes its title from the last lecture by Allen Newell, one of the pioneers of cognitive science. He said, “The question for me is how can the human mind occur in the physical universe? We now know that the world is governed by physics. We now understand the way biology nestles comfortably within that. The issue is how will the mind do that as well?” Newell argued that the answer to his question must take the form of a cognitive architecture, and this book describes an answer that is emerging from the study of brain and behavior. Humans share the same basic cognitive architecture with all primates, but they have evolved abilities to exercise abstract control over cognition and process more complex relational patterns. The human cognitive architecture consists of a set of largely independent modules associated with different brain regions. The book discusses in detail how these various modules can combine to produce behaviors as varied as driving a car and solving an algebraic equation, but focuses principally on two of the modules: declarative and procedural. The declarative module involves a memory system that, moment by moment, attempts to give each person the most appropriate possible window into his or her past. The procedural module involves a central system that strives to develop a set of productions that will enable the most adaptive response from any state of the modules.Less
This book takes its title from the last lecture by Allen Newell, one of the pioneers of cognitive science. He said, “The question for me is how can the human mind occur in the physical universe? We now know that the world is governed by physics. We now understand the way biology nestles comfortably within that. The issue is how will the mind do that as well?” Newell argued that the answer to his question must take the form of a cognitive architecture, and this book describes an answer that is emerging from the study of brain and behavior. Humans share the same basic cognitive architecture with all primates, but they have evolved abilities to exercise abstract control over cognition and process more complex relational patterns. The human cognitive architecture consists of a set of largely independent modules associated with different brain regions. The book discusses in detail how these various modules can combine to produce behaviors as varied as driving a car and solving an algebraic equation, but focuses principally on two of the modules: declarative and procedural. The declarative module involves a memory system that, moment by moment, attempts to give each person the most appropriate possible window into his or her past. The procedural module involves a central system that strives to develop a set of productions that will enable the most adaptive response from any state of the modules.
John C. Lennox and Derek J. S. Robinson
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198507284
- eISBN:
- 9780191709326
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507284.003.0007
- Subject:
- Mathematics, Pure Mathematics
This chapter discusses simple modules over polycyclic groups, the Jategaonkar-Roseblade theorem, the Artin-Rees property, and residual finiteness. It also talks about the Frattini subgroup.
This chapter discusses simple modules over polycyclic groups, the Jategaonkar-Roseblade theorem, the Artin-Rees property, and residual finiteness. It also talks about the Frattini subgroup.
John R. Anderson
- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780195324259
- eISBN:
- 9780199786671
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195324259.003.0002
- Subject:
- Psychology, Cognitive Models and Architectures
This chapter describes how the mind — faced with high demands of functioning in the world and the processing constraints of the brain — has developed a structure in which different cognitive ...
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This chapter describes how the mind — faced with high demands of functioning in the world and the processing constraints of the brain — has developed a structure in which different cognitive functions are performed by different modules and integrated through a central system. A set of eight information-processing modules and the brain regions with which they are associated are described: a visual module in the fusiform gyrus; an aural module in the auditory cortex; a manual and vocal module along the motor strip; a retrieval module in the prefrontal cortex; a goal module in the anterior cingulate; an imaginal module in the posterior parietal cortex; and a procedural module in the basal ganglia. Three examples that illustrate their function are described: a study of time sharing while driving; a laboratory study of perfect time sharing; and an fMRI brain imaging study that activates all eight modules.Less
This chapter describes how the mind — faced with high demands of functioning in the world and the processing constraints of the brain — has developed a structure in which different cognitive functions are performed by different modules and integrated through a central system. A set of eight information-processing modules and the brain regions with which they are associated are described: a visual module in the fusiform gyrus; an aural module in the auditory cortex; a manual and vocal module along the motor strip; a retrieval module in the prefrontal cortex; a goal module in the anterior cingulate; an imaginal module in the posterior parietal cortex; and a procedural module in the basal ganglia. Three examples that illustrate their function are described: a study of time sharing while driving; a laboratory study of perfect time sharing; and an fMRI brain imaging study that activates all eight modules.
S. K. Jain, Ashish K. Srivastava, and Askar A. Tuganbaev
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199664511
- eISBN:
- 9780191746024
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199664511.003.0005
- Subject:
- Mathematics, Algebra
This chapter considers rings each of whose proper cyclic modules is injective and prove theorems of Faith, Cozzens, and Damiano.
This chapter considers rings each of whose proper cyclic modules is injective and prove theorems of Faith, Cozzens, and Damiano.
S. K. Jain, Ashish K. Srivastava, and Askar A. Tuganbaev
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199664511
- eISBN:
- 9780191746024
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199664511.003.0007
- Subject:
- Mathematics, Algebra
This chapter's first section deals with rings each of whose cyclic modules is quasi-injective. Section 2 wich follows discusses rings over which each proper cyclic module is quasi-injective.
This chapter's first section deals with rings each of whose cyclic modules is quasi-injective. Section 2 wich follows discusses rings over which each proper cyclic module is quasi-injective.
