Modules and Rings

Couverture
Cambridge University Press, 28 oct. 1994 - 442 pages
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.
 

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Table des matières

MODULES
1
FREE MODULES
19
INJECTIVE MODULES
30
TENSOR PRODUCTS
53
CERTAIN IMPORTANT ALGEBRAS
71
SIMPLE MODULES
86
THE JACOBSON RADICAL
111
SUBDIRECT PRODUCT
140
HEREDITARY RINGS FREE
269
MODULE CONSTRUCTIONS
283
CATEGORIES AND FUNCTORS
298
MODULE CATEGORIES
335
FLAT MODULES
359
PURITY
367
APPENDIX A BASICS
398
APPENDIX B CERTAIN IMPORTANT ALGEBRAS
412

PRIMES AND SEMIPRIMES
148
PROJECTIVE MODULES AND MORE
163
DIRECT SUM DECOMPOSITIONS
204
SIMPLE ALGEBRAS
239
LIST OF SYMBOLS AND NOTATION
427
SUBJECT INDEX
436
AUTHOR INDEX
442
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