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内容简介

　　《代数学基础》论述代数学及其在现代数学和科学中的地位，高度原创且内容充实。作者通过讨论大学代数课程，如李群、上同调、范畴论等，阐述每个代数概念的起源与物理现象及其他数学分支之间的联系。《代数学基础》为数学家必读，无论他是初学代数学还是代数学专家。

目录

Preface
1．What is Algebra？
2．Fields
3．Commutative Rings
4．Homomorphisms and Ideals
5．Modules
6．Algebraic Aspects of Dimension
7．The Algebraic View of Infinitesimal Notions
8．Noncommutative Rings
9．Modules over Noncommutative Rings
10．Semisimple Modules and Rings
11．Division Algebras of Finite Rank
12．The Notion of a Group
13．Examples of Groups： Finite Groups
14．Examples of Groups： Infinite Discrete Groups
15．Examples of Groups： Lie Groups and Algebraic Groups
16．General Results of Group Theory
17．Group Representations
A．Representations of Finite Groups
B．Representations of Compact Lie Groups
18．Some Applications of Groups
A．Galois Theory
B．The Galois Theory of Linear Differential Equations （Picard Vessiot Theory）
C．Classification of Unramified Covers
D．Invariant Theory
E．Group Representations and the Classification of Elementary Particles
19．Lie Algebras and Nonassociative Algebra
A．Lie Algebras
B．Lie Theory
C．Applications of Lie Algebras
D．Other Nonassociative Algebras
20．Categories
21．Homological Algebra
A．Topological Origins of the Notions of Homological Algebra
B．Cohomology of Modules and Groups
C．Sheaf Cohomology
22．K—theory
A．Topological K—theory
B．Algebraic K—theory
Comments on the Literature
References
Index of Names
Subject Index

前言/序言

代数学基础 [Basic Notions Of Algebra] 电子书 下载 mobi epub pdf txt

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