Modules and Rings

ISBN-13: 9780521462587 / Angielski / Twarda / 1994 / 464 str.

John Dauns

Opis

This book on modern module and non-commutative ring theory starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. 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.

Recenzje

"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

Spis treści

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.