Modules and Rings

Modules and Rings

by John Dauns
     
 

ISBN-10: 0521063485

ISBN-13: 9780521063487

Pub. Date: 05/29/2008

Publisher: Cambridge University Press

This book on modern module and non-commutative ring theory is ideal for beginning graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. Students will have the chance to develop proofs, solve problems, and to find interesting questions. The first half of…  See more details below

Overview

This book on modern module and non-commutative ring theory is ideal for beginning graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. Students will have the chance to develop proofs, solve problems, and to find interesting questions. The first half of the book is concerned with free, projective, and injective modules, tensor algebras, simple modules and primitive rings, the Jacobson radical, and subdirect products. Later in the book, more advanced topics, such as hereditary rings, categories and functors, flat modules, and purity are introduced. These later chapters will also prove a useful reference for researchers in non-commutative ring theory. Enough background material (including detailed proofs) is supplied to give the student a firm grounding in the subject.

Product Details

ISBN-13:
9780521063487
Publisher:
Cambridge University Press
Publication date:
05/29/2008
Pages:
464
Product dimensions:
5.90(w) x 8.90(h) x 1.20(d)

Related Subjects

Table of Contents

Preface
Note to the Reader
Ch. 1Modules1
Ch. 2Free Modules19
Ch. 3Injective Modules30
Ch. 4Tensor Products53
Ch. 5Certain Important Algebras71
Ch. 6Simple Modules and Primitive Rings86
Ch. 7The Jacobson Radical111
Ch. 8Subdirect Product Decompositions140
Ch. 9Primes and Semiprimes148
Ch. 10Projective Modules and More on Wedderburn Theorems163
Ch. 11Direct Sum Decompositions204
Ch. 12Simple Algebras239
Ch. 13Hereditary Rings. Free and Projective Modules269
Ch. 14Module Constructions283
Ch. 15Categories and Functors298
Ch. 16Module Categories335
Ch. 17Flat Modules359
Ch. 18Purity367
Appendix A: Basics398
Appendix B: Certain Important Algebras412
List of Symbols and Notation427
Bibliography432
Subject Index436
Author Index442

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