Basic notions of algebra.代数学新发明
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作者： Igor R. Shafarevich，Aleksej I. Kostrikin著
出 版 社： 北京燕山出版社
出版时间： 2005-6-1字数：版次： 1页数： 258印刷时间： 2005/06/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783540251774包装： 精装内容简介
This book is wholeheartedly recommended to every student or user of mathematics. Although the author modestly describes his book as 'merely an attempt to talk about' algebra, he succeeds in writing an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields, commutative rings and groups studied in every university math course, through Lie groups and algebras to cohomology and category theory, the author shows how the origins of each algebraic concept can be related to attempts to model phenomena in physics or in other branches of mathematics. Comparable in style with Hermann Weyl's evergreen essay The Classical Groups, Shafarevich's new book is sure to become required reading for mathematicians, from beginners to experts.
目录
Preface
1.What is Algebra?
2.Fields
3.Commutative Rings
4.Homomorphisms and Ideals
5.Modrles
6.Alegvraic Aspects of Dinension
7.The Algebraic View of Infinitesimal Notions
8.Noncommutative
9.Modules over Noncommutative Rings
10.Semisimple Modules and Rings
11.Division Algevras of Finite Rand
12.The Notion of a Group
13.Example of Grops:Finite Groups
14.Example of Grops:Infinite Discrete Groups
15.Example of Grops:Lie Groups and Algebraic Groups
16.General Results of Group Theotry
17.Group Repressentations
18.Some Applecations of Groups
19.Lie Algebras and Nonassociative Algebra
20.Categories
21.Homological Algebra
22.K-theory
Comments on the Literature
References
Index of Names
Subject Index