新書推薦:
《
女性与疯狂(女性主义里程碑式著作,全球售出300万册)
》
售價:HK$
109.8
《
药食同源中药鉴别图典
》
售價:HK$
67.0
《
设计中的比例密码:建筑与室内设计
》
售價:HK$
87.4
《
冯友兰和青年谈心系列:看似平淡的坚持(哲学大师冯友兰和年轻人谈心,为人处事)
》
售價:HK$
55.8
《
汉字理论与汉字阐释概要 《说解汉字一百五十讲》作者李守奎新作
》
售價:HK$
76.2
《
汗青堂丛书144·决战地中海
》
售價:HK$
168.0
《
逝去的武林(十周年纪念版 武学宗师 口述亲历 李仲轩亲历一九三零年代武人言行录)
》
售價:HK$
54.9
《
唐代冠服图志(百余幅手绘插画 图解唐代各类冠服 涵盖帝后 群臣 女官 士庶 军卫等 展现唐代社会风貌)
》
售價:HK$
87.4
|
內容簡介: |
ThepresentVrolumecompletestheseriesoftextsonalgebrawhichtheauthorbeganmorethantenyearsago.TheaccountoffieldtheoryandGaloistheorywhichwegirrehereisbasedonthenotionsandresultsofgeneralalgebrawhichappearinourfirstvolumeandonthemoreelementarypartsofthesecondvolume,dealingwithlinearalgebra.Thelevelofthepresentwork.isroughlythesameasthatofVolumeII.
|
目錄:
|
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
|
|