Algebra代数学
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作者： Thomas W. Hungerford 著
出 版 社：
出版时间： 2003-2-14字数：版次： 1页数： 502印刷时间： 2003/02/14开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387905181包装： 精装内容简介
Algebra fulfills a definite need to provide a self-contained, one volume, graduate level algebra text that is readable by the average graduate student and flexible enough to accomodate a wide variety of instructors and course contents. The guiding philosophical principle throughout the text is that the material should be presented in the maximum usable generality consistent with good pedagogy. Therefore it is essentially self-contained, stresses clarity rather than brevity and contains an unusually large number of illustrative exercises. The book covers major areas of modern algebra, which is a necessity for most mathematics students in sufficient breadth and depth.
目录
Preface
Acknowledgments
Suggestions on the Use ofThis Book
Introductions：Prerequisites and Preliminaries
1．Logic
2．Sets and Classes
3．Functions
4．Relations and Partitions
5．Products．
6．The Integers
7．The Axiom of Choice，Order and Zorn’S Lemma
8．Cardinal Numbers
ChapterⅠ：Groups
1．Semigroups．Monoids and Groups
2．Homomorphisms and Subgroups．
3．Cyclic Groups．
4．Cosets and Countin9。
5．Normality，Quotient Groups，and Homomorphisms：
6．Symmetric，Alternatin9，and Dihedral Groups
7．Categories：Products，Coproducts，and Free Objects
8．DirectProducts andDirect Sums．
9．Free Groups，Free Products，Generators&Relations
Chapter Ⅱ：The Structure of Groups．
1．Free Abelian Groups
2．Finitely Generated Abelian Groups。
3．The KruU．Schmidt Theorem．
4．The Action ofa Group on a Set
5．The Sylow Theorems．
6．Classification of Finite Groups
7．Nilpotent and Solvable Groups
8．Normal and Subnormal Series
Chapter Ⅲ：Rings
1．Rings and Homomorphisms．
2． Ideals
3．Factorization in Commutative Rings
4．Rings of Quotients and Localization
5．Rings of Polynomials and Formal Power Series
6．Factorization in Polynomial Rings．
Chapter ⅣModules
1．Modules．Homomorphisms and Exact Sequences．
2．Free Modules and Vector Spaces
3．Ptojective and Injective Modules
4．Hom and Duality
5．Tensor Products．
6．Modules over aPrincipalIdealDomain．
7．Algebras
Chapter ⅤFields and Galois Theory
1．Field Extensions Appendix：Ruler and Compass Constructions．
2．The Fundamental Theorem Appendix：Symmetric Rational Functions
3．Splitting Fields．Algebraic Closure and Normality Appendix：The Fundamental Theorem of Algebra
4．The Galois Group ofa Polynomial
5．Finite Fields
6．Separability．
7．Cyclic Extensions．
8．Cyclotomic Extensions
9．Radical Extensions Appendix：The General Equation of Degree n
Chapter Ⅵ：The Structure of Fields
1．Transcendence Bases．
2．Linear Disjointness and Separability
Chapter ⅦLinear algebra
Chapter Ⅷ Commutative Rings and Modules
Chapter Ⅸ The structure of rings
Chapter Ⅹ Categories
INDEX
