抽象代数讲义（第3卷）（英文）

图书标准信息

• 作者 [德]雅格布斯（Jacobson N.） 著
• 出版社 世界图书出版公司
• 出版时间 2013-10
• 版次 1
• ISBN 9787510061530
• 定价 69.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 323页
• 正文语种 英语

【内容简介】

　　ThepresentVrolumecompletestheseriesoftextsonalgebrawhichtheauthorbeganmorethantenyearsago.TheaccountoffieldtheoryandGaloistheorywhichwegirrehereisbasedonthenotionsandresultsofgeneralalgebrawhichappearinourfirstvolumeandonthemoreelementarypartsofthesecondvolume，dealingwithlinearalgebra.Thelevelofthepresentwork.isroughlythesameasthatofVolumeII.

【目录】

INTRODUCTION
SECTION
1.Extensionofhomomorphisms
2.Algebras
3.Tensorproductsofvectorspaces
4.Tensorproductofalgebras

CHAPTERI:FINITEDIMENSIONALEXTENSIONFIELDS
1Somevectorspacesassociatedwithmappingsoffields
2.TheJacobson-Bourbakicorrespondence
3.Dedekindindependencetheoremforisomorphismsofafield
4.Finitegroupsofautomorphisms.
5.Splittingfieldofapolynomial
6.Multipleroots.Separablepolynomials
7.The"fundamentaltheorem"ofGaloistheory
8.Normalextensions.Normalclosures
9.Structureofalgebraicextensions.Separability
10.Degreesofseparabilityandinseparability.Structureofnormalextensions
11.Primitiveelements
12.Normalbases
13.Finitefields
14.Regularrepresentation,traceandnorm
15.Galoiscohomology
16.Compositesoffields

CHAPTERII:GALOISTHEORYOFEQUATIOIVS
1.TheGaloisgroupofanequation
2.Pureequations
3.Galois'criterionforsolvabilitybyradicals
4.Thegeneralequationofn-thdegree
5.EquationswithrationalcoefficientsandsymmetricgroupasGaloisgroup

CHAPTERⅢ:ABELIANEXTENSlONS
1.Cyclotomicfieldsovertherationals
2.Charactersoffinitecommutatiyegroups
3.Kummerextensions
4.Wittrrectors
5.Abelianp-extensions

CHAPTERⅣ:STRUCTURETHEORYOFFIELDS
1Algebraicallyclosedfields
2.InfiniteGaloistheory
3.Transcendencybasis
4.Luroth'stheorem.
5.Lineardisjointnessandseparatingtranscendencybases
6.Derivations
7.Derivations,separabilityandp-independence
8.Galoistheoryforpurelyinseparableextensionsofexponertone
9.Higherderivations
10.Tensorproductsoffields
11.Freecompositesoffields

CHAPTERV:VALUATION.THEORY
1.Realvaluations
2.Realvaluationsofthefieldofrationalnumbers
3.Realvaluationsof（x）whicharetrivialin
4.Completionofafield
5.Somepropertiesofthefieldofp-adicnumbers
6.Hensel'slemma
7.Constructionofcompletefieldswithgivenresiduefields
8.Orderedgroupsand-valuations
9.Valuations,valuationrings,andplaces
10.Characterizationofrealnon-archimedeanvaluations
11.Extensionofhomomorphismsandvaluations
12.Applicationoftheextensiontheorem:HilbertNullstellensatz
13.Applicationoftheextensiontheorem:integralclosure
……

CHAPTERVI:ARTIN-SCHREIERTHEORY
Index