抽象代数基本教程
2008-11
菲来 (Fraleigh.J.B) 世界图书出版公司 (2008-11出版)
菲来
520
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本书是一部介绍抽象代数的入门书籍。假定学生了解了微积分和线性代数，并且理论大都在书中以例子和练习的形式出现。该书旨在教给学生尽可能多的群，环，以及域理论，最大特点是包含了较多的扎实的基础部分，这些部分对于更进一步的学习代数是有很大的帮助的。为了满足更多读者的要求，本书包含了很多有关拓扑中的同调群，同调群的计算以加深对因子群的理解。书中内容浅显易懂，为了将同调群讲述的更加清楚，在第6版的基础上减少了自动机，二进制线性密码以及部分代数结构。书后面附有不少练习，这些加深学生对内容的理解。 目次：群与子群；排列，陪集和直积；同态和因子群；环和域；理想和因子环；扩展域；高等群论；拓扑群；因子分解；自同态和伽罗瓦理论。
作者：(美国)菲来 (Fraleigh.J.B)
Instructor's PrefaceStudent's Preface Dependence Chart Sets and RelationsⅠ GROUPS AND SUBGROUPSIntroduction and ExamplesBinary OperationsIsomorphic Binary StructuresGroupsSubgroupsCyclic GroupsGenerating Sets and Cayley DigraphsⅡ PERMUTATIONS, COSETS, AND DIRECT PRODUCTSGroups of PermutationsOrbits, Cycles, and the Alternating GroupsCosets and the Theorem of LagrangeDirect Products and Finitely Generated Abelian GroupsPlane IsometriesⅢ HOMOMORPHISMS AND FACTOR GROUPSHomomorphismsFactor GroupsFactor-Group Computations and Simple GroupsGroup Action on a SetApplications of G-Sets to CountingⅣ RINGS AND FIELDSRings and FieldsIntegral DomainsFermat's and Euler's TheoremsThe Field of Quotients of an Integral Domain Rings of PolynomialsFactorization of Polynomials over a FieldNoncommutative ExamplesOrdered Rings and FieldsⅤ IDEALS AND FACTOR RINGSHomomorphisms and Factor RingsPrime and Maximal IdealsGrobner Bases for IdealsⅥ EXTENSION FIELDSIntroduction to Extension FieldsVector SpacesAlgebraic ExtensionsGeometric Constructions Finite FieldsⅦ ADVANCED GROUP THEORYIsomorphism TheoremsSeries of GroupsSylow TheoremsApplications of the Sylow TheoryFree Abelian GroupsFree GroupsGroup PresentationsⅧ GROUPS IN TOPOLOGYSimplicial Complexes and Homology GroupsComputations of Homology GroupsMore Homology Computations and ApplicationsHomological AlgebraⅨ FACTORIZATIONUnique Factorization DomainsEuclidean DomainsGaussian Integers and Multiplicative NormsⅩ AUTOMORPHISMS AND GALOIS THEORYAutomorphisms of FieldsThe Isomorphism Extension TheoremSplitting FieldsSeparable ExtensionsTotally Inseparable Extensions Galois TheoryIllustrations of Galois TheoryCyclotomic ExtensionsInsolvability of the QuinticAppendix: Matrix AlgebraBibliographyNotationsAnswers to Odd-Numbered Exercises Not Asking for Definitions or ProofsIndex
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《抽象代数基本教程(第7版)》由世界图书出版公司出版。
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严重质量问题，退货了！
内容组织的还是不错的，篇幅稍微长了点，加些模的内容就更好了。
你妹的世图，就知道糟蹋书，字体这么小，根本没法看。直接给退了。
UCB数学系用书..........
结构清晰，很有条理，例子详实；纸张质量比较糟糕。
很好的参考书,写的浅显易懂,与别的经典(lang,hungeford,artin)一起看会起到事半功倍的效果.