代數(shù)學

內容概要

　　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．

書籍目錄

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 NumbersChapter 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 SnChapter 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 IdealsChapter 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 TheoryChapter 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 TheoremAppendix  A1 Set Theoretical Notations  A2 Peano's Axioms  A3 Homological AlgebraIndex

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