| 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 Ⅶ Linear algebra Chapter Ⅷ Commutative Rings and Modules Chapter Ⅸ The structure of rings Chapter Ⅹ Categories INDEX |
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