An introduction to rings and modules : with K-theory in view
著者
書誌事項
An introduction to rings and modules : with K-theory in view
（Cambridge studies in advanced mathematics, v. 65）
Cambridge University Press, 2000
- : hardback
大学図書館所蔵 件 / 全68件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. [252]-256) and index
内容説明・目次
内容説明
This book, first published in 2000, is a concise introduction to ring theory, module theory and number theory, ideal for a first year graduate student, as well as an excellent reference for working mathematicians in other areas. Starting from definitions, the book introduces fundamental constructions of rings and modules, as direct sums or products, and by exact sequences. It then explores the structure of modules over various types of ring: noncommutative polynomial rings, Artinian rings (both semisimple and not), and Dedekind domains. It also shows how Dedekind domains arise in number theory, and explicitly calculates some rings of integers and their class groups. About 200 exercises complement the text and introduce further topics. This book provides the background material for the authors' companion volume Categories and Modules, soon to appear. Armed with these two texts, the reader will be ready for more advanced topics in K-theory, homological algebra and algebraic number theory.
目次
- 1. Basics
- 2. Direct sums and their short exact sequences
- 3. Noetherian rings and polynomial rings
- 4. Artinian rings and modules
- 5. Dedekind domains
- 6. Modules over Dedekind domains.
「Nielsen BookData」 より