Modules and Rings

A book on module and non-commutative ring theory for graduate students.

John Dauns (Author)

9780521063487, Cambridge University Press

Paperback / softback, published 29 May 2008

464 pages, 147 b/w illus. 3 tables
22.8 x 15.2 x 2.6 cm, 0.7 kg

"Dauns...is always intensely focused on the big picture; there is no chance that the reader will lose sight of what is important or where the stroy is going. He is equally meticulous about details; his explanations are finely crafted and complete...[the book] will be the salvation of many a graduate student preparing for qualifying exams." D.V. Feldman, Choice

This book on modern 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.

1. Modules
2. Free modules
3. Injective modules
4. Tensor products
5. Certain important algebras
6. Simple modules and primitive rings
7. The Jacobson radical
8. Subdirect product decompositions
9. Primes and semiprimes
10. Projective modules and more on Wedderburn theorems
11. Direct sum decompositions
12. Simple algebras
13. Hereditary rings, free and projective modules
14. Module constructions
15. Categories and functors
16. Module categories
17. Flat modules
18. Purity.

Subject Areas: Algebra [PBF]