《非交換環初級教程》是2010年12月1日清華大學出版社出版的圖書，作者是拉姆（T.Y.Lam）。本書介紹了韋德伯恩-Artin基本理論、雅各布森激進理論、組和代數表示理論知識，是一本研究生學習參考用書。
基本介紹
- 書名：非交換環初級教程
- 頁數：385頁
- 出版時間：第1版 (2010年12月1日)
- 裝幀：平裝
圖書信息,作者簡介,內容簡介,
圖書信息
出版社: 清華大學出版社;
外文書名: A First Course in Noncommutative Rings(Second Edition)
叢書名: 數學圖書影印版系列
:
正文語種: 英語
開本: 16
ISBN: 9787302241515, 7302241511
條形碼: 9787302241515
尺寸: 22.8 x 18.2 x 1.6 cm
重量: 522 g
作者簡介
作者：（美國）拉姆（T.Y.Lam）
內容簡介
《非交換環初級教程(第2版)》
A First Course in Noncommutative Rings, an outgrowth of the author' s lectures at the University of California at Berkeley, is intended as a textbook for a one-semester course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semisimple rings, Jacobson' s theory of the radical, representation theory of groups and algebras, prime and semiprime rings, primitive and semiprimitive rings, division rings, ordered rings, local and semilocal rings, perfect and semiperfect rings, and so forth. By aiming the level of writing at the novice rather than the connoisseur and by stressing the role of examples and motivation, the author has produced a text that is suitable not only for use in a graduate course, but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition
.在非交換環的第一門課程，在加州大學伯克利分校的作者講座的產物，目的是作為一個理論基礎環一一學期課程的教科書。該材料包括半單環的韋德伯恩-Artin理論，雅各布森的激進理論，組和代數的表示理論，素和半素環，原始的和半本原環，除環，有序環，本地和半局部環，完美的和半完全環，等等。針對在新手而不是行家和突出的例子和動力作用的寫作水平，筆者產生了一個文本，不僅適用於用在研究生的課程，也為有興趣的研究生在課題學習。400多練習測試文本中的一般理論的理解都包含在這個新的版本。
目錄
preface to the second edition
preface to the first edition
notes to the reader
chapter 1 wedderburn-artin theory
1.basic terminology and examples
exercises for 1
2.semisimplicity
exercises for 2
3.structure of semisimple rings
exercises for 3
chapter 2 jacobson radical theory
4.the jacobson radical
exercises for 4
5.jacobson radical under change of rings.
exercises for 5
6.group rings and the j-semisimplicjty problem
exercises for 6
chapter 3 introduction to representation theory
7.modules over finite-dimensional algebras
exercises for 7
8.representations of groups
exercises for 8
9.linear groups
exercises for 9
chapter 4 prime and primitive rings
10. the prime radical; prime and semiprime rings
exercises for 10
11. structure of primitive rings; the density theorem
exercises for 11
12. subdirect products and commutativity theorems
exercises for 12
chapter 5 introduction to division rings
13. division rings
exercises for 13
14. some classical constructions
exercises for 14
15. tensor products and maximal subfields
exercises for 15
16. polynomials over division rings
exercises for 16
chapter 6 ordered structures in rings
17. orderings and preorderings in rings
exercises for 17
18. ordered division rings
exercises for 18
chapter 7 local rings, semilocai rings, and idempotents
19. local rings
exercises for 19
20. semilocal rings
appendix: endomorphism rings of uniserial modules
exercises for 20
21. th theory ofidempotents
exercises for 21
22. central idempotents and block decompositions
exercises for 22
chapter 8 perfect and semiperfect rings
23. perfect and semiperfect rings
exercises for 23
24. homoiogical characterizations of perfect and semiperfect rings
exercises for 24
25. principal indecomposables and basic rings
exercises for 25
references
name index
subject index
