Exercises in Classical Ring Theory

Couverture
Springer Science & Business Media, 29 juin 2013 - 288 pages
Based in large part on the comprehensive "First Course in Ring Theory" by the same author, this book provides a comprehensive set of problems and solutions in ring theory that will serve not only as a teaching aid to instructors using that book, but also for students, who will see how ring theory theorems are applied to solving ring-theoretic problems and how good proofs are written.
The author demonstrates that problem-solving is a lively process: in "Comments" following many solutions he discusses what happens if a hypothesis is removed, whether the exercise can be further generalized, what would be a concrete example for the exercise, and so forth. The book is thus much more than a solution manual.
 

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Table des matières

Preface
1
2 Semisimplicity
16
Jacobson Radical Theory
35
5 Jacobson radical under change of rings
52
Introduction to Representation Theory
69
9 Linear groups
98
Prime and Primitive Rings 103
102
11 Structure of primitive rings the Density Theorem
119
Introduction to Division Rings
151
15 Tensor products and maximal subfields
176
Ordered Structures in Rings
191
Local Rings Semilocal Rings
211
21 The theory of idempotents
229
22 Central idempotents and block decompositions
250
24 Homological characterizations of perfect
265
Subject Index
281

12 Subdirect products and commutativity theorems
136

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