# Exercises in Basic Ring Theory

Springer Science & Business Media, Mar 9, 2013 - Mathematics - 200 pages
Each undergraduate course of algebra begins with basic notions and results concerning groups, rings, modules and linear algebra. That is, it begins with simple notions and simple results. Our intention was to provide a collection of exercises which cover only the easy part of ring theory, what we have named the "Basics of Ring Theory". This seems to be the part each student or beginner in ring theory (or even algebra) should know - but surely trying to solve as many of these exercises as possible independently. As difficult (or impossible) as this may seem, we have made every effort to avoid modules, lattices and field extensions in this collection and to remain in the ring area as much as possible. A brief look at the bibliography obviously shows that we don't claim much originality (one could name this the folklore of ring theory) for the statements of the exercises we have chosen (but this was a difficult task: indeed, the 28 titles contain approximatively 15.000 problems and our collection contains only 346). The real value of our book is the part which contains all the solutions of these exercises. We have tried to draw up these solutions as detailed as possible, so that each beginner can progress without skilled help. The book is divided in two parts each consisting of seventeen chapters, the first part containing the exercises and the second part the solutions.

### What people are saying -Write a review

We haven't found any reviews in the usual places.

### Contents

 Zero Divisors 15 Division Rings 31 Socle and Radical 45 Semisimple Rings 49 Prime Ideals Local Rings 53 Polynomial Rings 59 Rings of Quotients 63 Rings of Continuous Functions 67
 Ring Homomorphisms 107 Characteristics 111 Divisibility in Integral Domains 115 Division Rings 121 Automorphims 127 The Tensor Product 133 Artinian and Noetherian Rings 139 Socle and Radical 145

 Special Problems 73 SOLUTIONS 77 Fundamentals 79 Ideals 91 Zero Divisors 101
 Semisimple Rings 153 Prime Ideals Local Rings 159 Polynomial Rings 169 Special problems 187 Copyright