代數學基礎 [Basic Notions Of Algebra] pdf epub mobi txt 電子書 下載 2024

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內容簡介

　　《代數學基礎》論述代數學及其在現代數學和科學中的地位，高度原創且內容充實。作者通過討論大學代數課程，如李群、上同調、範疇論等，闡述每個代數概念的起源與物理現象及其他數學分支之間的聯係。《代數學基礎》為數學傢必讀，無論他是初學代數學還是代數學專傢。

目錄

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

代數學基礎 [Basic Notions Of Algebra] 下載 mobi epub pdf txt 電子書

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