抽象代数：海外优秀数学类教材系列丛书

图书标准信息

• 作者 罗特曼 著
• 出版社 高等教育出版社
• 出版时间 2004-12
• 版次 1
• ISBN 9787040155563
• 定价 68.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 1012页
• 正文语种 简体中文，英语

【内容简介】

Thisbookcanbeusedasatextforthefirstyearofgraduatealgebra,butitismuchmorethanthat.Itcanalsoservemoreadvancedgraduatestudentswishingtolearntopicsontheirown;whilenotreachingthefrontiers,thebookdoesprovideasenseofthesuccessesandmethodsarisinginanarea.Finally,thisisareferencecontainingmanyofthestandardtheoremsanddefinitionsthatusersofalgebraneedtoknow.Thus,thebookisnotonlyanappetizer,butaheartymealaswell.

【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《A First Course in Abstract Algebra》(抽象代数基础教程，本书影印版、中文版由机械工业出版社引进出版)、《Galois Theory》等。

【目录】

Preface

Etymology

SpecialNotation

ChapterIThingsPast

1.1.SomeNumberTheory

1.2.RootsofUnity

1.3.SomeSetTheory

Chapter2GroupsI

2.1.Introduction

2.2.Permutations

2.3.Groups

2.4.LagrangesTheorem

2.5.Homomorphisms

2.6.QuotientGroups

2.7.GroupActions

Chapter3CommutativeRingsI

3.1.Introduction

3.2.FirstProperties

3.3.Polynomials

3.4.GreatestCommonDivisors

3.5.Homomorphisms

3.6.EuclideanRings

3.7.LinearAlgebra

VectorSpaces

LinearTransformations

3.8.QuotientRingsandFiniteFields

Chapter4Fields

4.1.InsolvabilityoftheQuintic

FormulasandSolvabilitybyRadicals

TranslationintoGroupTheory

4.2.FundamentalTheoremofGaloisTheory

Chapter5GroupsII

5.1.FiniteAbelianGroups

DirectSums

BasisTheorem

FundamentalTheorem

5.2.TheSylowTheorems

5.3.TheJordan-HilderTheorem

5.4.ProjectiveUnimodularGroups

5.5.Presentations

5.6.TheNeilsen-SchreierTheorem

Chapter6CommutativeRingsH

6.1.PrimeIdealsandMaximalIdeals

6.2.UniqueFactorizationDomains

6.3.NoetherianRings

6.4.ApplicationsofZomsLemma

6.5.Varieties

6.6.Gr6bnerBases

GeneralizedDivisionAlgorithm

BuchbergersAlgorithm

Chapter7ModulesandCategories

7.1.Modules

7.2.Categories

7.3.Functors

7.4.FreeModules,Projectives,andInjectives

7.5.GrothendieckGroups

7.6.Limits

Chapter8Algebras

8.1.NoncommutativeRings

8.2.ChainConditions

8.3.SemisimpleRings

8.4.TensorProducts

8.5.Characters

8.6.TheoremsofBurnsideandofFrobenius

Contents

Chapter9AdvancedLinearAlgebra

9.1.ModulesoverPIDs

9.2.RationalCanonicalForms

9.3.JordanCanonicalForms

9.4.SmithNormalForms

9.5.BilinearForms

9.6.GradedAlgebras

9.7.DivisionAlgebras

9.8.ExteriorAlgebra

9.9.Determinants

9.10.LieAlgebras

Chapter10Homology

10.1.Introduction

10.2.SemidirectProducts

10.3.GeneralExtensionsandCohomology

10.4.HomologyFunctors

10.5.DerivedFunctors

10.6.ExtandTor

10.7.CohomologyofGroups

10.8.CrossedProducts

10.9.IntroductiontoSpectralSequences

Chapter11CommutativeRingsIII

11.1.LocalandGlobal

11.2.DedekindRings

Integrality

NullstellensatzRedux

AlgebraicIntegers

CharacterizationsofDedekindRings

FinitelyGeneratedModulesoverDedekindRings

11.3.GlobalDimension

11.4.RegularLocalRings

AppendixTheAxiomofChoiceandZornsLemma

Bibliography

Index