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Hilbert Modular Forms and Iwasawa Theory

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 ... More


Cyclic Modules and the Structure of Rings

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 ... More


C*-modules and operator spaces

David P. Blecher and Christian Le Merdy

in Operator Algebras and Their Modules: An operator space approach

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 ... More


Basic theory of operator modules

David P. Blecher and Christian Le Merdy

in Operator Algebras and Their Modules: An operator space approach

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 ... More


The Case for Massively Modular Models of Mind

Peter Carruthers

in The Architecture of the Mind

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 ... More


The Architecture of Animal Minds

Peter Carruthers

in The Architecture of the Mind

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 ... More


Distinctively Human Practical Reason

Peter Carruthers

in The Architecture of the Mind

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 ... More


Modularity and Relevance: How Can a Massively Modular Mind Be Flexible and Context‐Sensitive? *

Dan Sperber

in The Innate Mind: Structure and Contents

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 ... More


Language and the Development of Spatial Reasoning *

Anna Shusterman and Elizabeth Spelke

in The Innate Mind: Structure and Contents

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. ... More


Perceptual Systems and Perceptual Beliefs

Jack C. Lyons

in Perception and Basic Beliefs: Zombies, Modules and the Problem of the External World

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 ... More


Cognitive Load and Human Decision, or, Three Ways of Rolling the Rock Uphil l

Kim Sterelny

in The Innate Mind: Volume 2: Culture and Cognition

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, ... More


Religion's Innate Origins and Evolutionary Background

Scott Atran

in The Innate Mind: Volume 2: Culture and Cognition

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 ... More


THE 1333-DIMENSIONAL REPRESENTATION

A. A. Ivanov

in The Fourth Janko Group

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 ... More


MODULAR IWASAWA THEORY

Haruzo Hida

in Hilbert Modular Forms and Iwasawa Theory

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 ... More


Selfadjointness criteria

David P. Blecher and Christian Le Merdy

in Operator Algebras and Their Modules: An operator space approach

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 ... More


How Can the Human Mind Occur in the Physical Universe?

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 ... More


THE THEORY OF FINITELY GENERATED SOLUBLE GROUPS II

John C. Lennox and Derek J. S. Robinson

in The Theory of Infinite Soluble Groups

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.


The Modular Organization of the Mind

John R. Anderson

in How Can the Human Mind Occur in the Physical Universe?

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 ... More


Rings each of whose proper cyclic modules is injective

S. K. Jain, Ashish K. Srivastava, and Askar A. Tuganbaev

in Cyclic Modules and the Structure of Rings

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.


Rings each of whose (proper) cyclic modules is quasi‐injective

S. K. Jain, Ashish K. Srivastava, and Askar A. Tuganbaev

in Cyclic Modules and the Structure of Rings

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.


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