抽象代数基础教程

出版时间：2006-4  出版社：机械工业出版社  作者：罗特曼  页数：581  
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内容概要

　　《抽象代数基础教程（英文版·第3版）》系统地介绍了抽象代数的基础内容，包括群、环、域、模等，每一部分独立成章，本科生、研究生等不同层次的读者可以挑选阅读。书中范例丰富，风趣易懂；另外，每一小节后都配有一定数量、难易不等的习题，书后还附有解答与提示，便于教学和自学。　　与第2版相比，第3版的更新如下：　　阐述更清晰，表达更顺畅。　　在前五章中，最重要的节，小节，定义，定理，例子旁边加有箭头指示。　　包含了任意域上的线性代数的更多知识。　　增加了一节介绍分类平面上的楣（frieze）群。　　增加了100多道习题　　本书可供高等院校数学系师生及有关工程技术人员使用。

作者简介

　　Joseph J.Rotman美国伊利诺伊大学厄巴纳-尚佩恩分校数学系教授。他著有多部数学方面的书，其中包括《Adanced Modern Algebra》（高等近世代数，本书中文版由机械工业出版社引进出版），（Galois Theory）等。

书籍目录

Preface to the Third EditionSuggested SyllabiTo the ReaderChapter I Number TheorySection 1.1 InductionSection 1.2 Binomial Theorem and Complex NumbersSection 1.3 Greatest Common DivisorsSection 1.4 The Fundamental Theorem of Arithmetic Section 1.5 CongruencesSection 1.6 Dates and DaysChapter 2 Groups ISection 2.1 Some Set Theory FunctionsEquivalence RelationsSection 2.2 Permutations Section 2.3 GroupsSymmetrySection 2.4 Subgroups and Lagrange's Theorem Section 2.5 HomomorphismsSection 2.6 Quotient GroupsSection 2.7 Group ActionsSection 2.8 Counting with GroupsChapter 3 Commutative Rings ISection 3.1 First Properties Section 3.2 FieldsSection 3.3 PolynomialsSection 3.4 HomomorphismsSection 3.5 From Numbers to Polynomials .Euclidean RingsSection 3.6 Unique FactorizationSection 3.7 IrreducibilitySection 3.8 Quotient Rings and Finite FieldsSection 3.9 A Mathematical OdysseyLatin SquaresMagic SquaresDesign of ExperimentsProjective PlanesChapter 4 Linear AlgebraSection 4.1 Vector SpacesGaussian Elimination Section 4.2 Euclidean Constructions Section 4.3 Linear TransformationsSection 4.4 EigenvaluesSection 4.5 CodesBlock CodesLinear CodesDecodingChapter 5 FieldsSection 5.1 Classical FormulasViete's Cubic FormulaSection 5.2 Insolvability of the General QuinticFormulas and Solvability by Radicals Quadratics CubicsQuarticsTranslation into Group TheorySection 5,3 Epilog Chapter 6 Groups HSection 6.1 Finite Abelian GroupsSection 6.2 The Sylow TheoremsSection 6.3 Ornamental SymmetryChapter 7 Commutative Rings IISection 7.1 Prime Ideals and Maximal IdealsSection 7.2 Unique FactorizationSection 7.3 Noetherian RingsSection 7.4 VarietiesSection 7.5 Generalized Divison Algorithm .Monomial OrdersDivision AlgorithmSection 7.6 Grobner BasesAppendix A InequalitiesAppendix B PseudocodesHints for Selected ExercisesBibliographyIndex