# Exercises in Basic Ring Theory

• Grigore Cǎlugǎreanu
• Peter Hamburg
Book

Part of the Kluwer Texts in the Mathematical Sciences book series (TMS, volume 20)

1. Front Matter
Pages i-xiv
2. ### Exercises

1. Front Matter
Pages 1-1
2. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 3-8
3. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 9-14
4. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 15-17
5. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 19-21
6. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 23-25
7. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 27-30
8. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 31-33
9. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 35-36
10. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 37-40
11. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 41-44
12. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 45-47
13. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 49-51
14. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 53-57
15. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 59-61
16. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 63-65
17. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 67-72
18. Grigore Cǎlugǎreanu, Peter Hamburg
Pages 73-76
3. ### Solutions

1. Front Matter
Pages 77-77

### Introduction

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.

### Keywords

Lattice algebra associative ring commutative ring homomorphism ring theory topology

#### Authors and affiliations

• Grigore Cǎlugǎreanu
• 1
• Peter Hamburg
• 2
1. 1.“Babeş-Bolyai” UniversityCluj-NapocaRomania
2. 2.Fernuniversität GHHagenGermany

### Bibliographic information

• DOI https://doi.org/10.1007/978-94-015-9004-4