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出版社：世界图书出版公司

ISBN：9787506292634

版次：1

商品编码：10758848

包装：平装

外文名称：Algebra

开本：16开

出版时间：2009-01-01

用纸：胶版纸

页数：350

正文语种：英文

具体描述

内容简介

The present book comes from the first part of the lecture notes I used for a first-yeargraduate algebra course at the University of Minnesota，Purdue University，and PekingUniversity．The Chinese versions of these notes were published by The Peking UniversitvPress in 1986，and by Linking Publishing Co of Taiwan in 1987．

内页插图

Chapter Ⅰ Set theory and Number Theory
1 Set Theory
2 Unique Factorization Theorem
3 Congruence
4 Chinese Remainder Theorem
5 Complex Integers
6 Real Numbers and p-aclic Numbers

Chapter Ⅱ Group theory
1 Definitions
2 The Transformation Groups on Sets
3 Subgroups
4 Normal Subgroups and Inner Automorphisms
5 Automorphism Groups
6 p-Groups and Sylow Theorems
7 Jordan-Holder Theorem
8 Symmetric Group Sn

Chapter Ⅲ Polynomials
1 Fields and Rings
2 Polynomial Rings and Quotient Fields
3 Unique Factorization Theorem for Polynomials
4 Symmetric Polynomial, Resultant and Discriminant
5 Ideals

Chapter Ⅳ Linear Algebra
1 Vector Spaces
2 Basis and Dimension
3 Linear Transformation and Matrix
4 Module and Module over P.I.D
5 Jordan Canonical Form
6 Characteristic Polynomial
7 Inner Product and Bilinear form
8 Spectral Theory

Chapter Ⅴ Polynomials in One Variable and Field Theory
1 Algebraically Closed Field
2 Algebraic Extension
3 Algebraic Closure
4 Characteristic and Finite Field
5 Separable Algebraic Extension
6 Galois Theory
7 Solve Equation by Radicals
8 Field Polynomial and Field Discriminant
9 Luroth's Theorem
Appendix
A1 Set Theoretical Notations
A2 Peano's Axioms
A3 Homological Algebra
Index