新書推薦：
《
《古籍识小录》上下册
》
售價：HK$
512.6
《
西周基层地域组织研究
》
售價：HK$
63.8
《
中国土司制度史料集成（全十九册）
》
售價：HK$
5478.0
《
守护健康：纽约市公共卫生制度的构建（1866—1920）
》
售價：HK$
96.8
《
岩体边坡锚固结构体系安全性评价指标体系研究
》
售價：HK$
72.6
《
癌症幸存者的秘密
》
售價：HK$
50.2
《
专业主义 （美）大卫·梅斯特
》
售價：HK$
86.9
《
城市计算 郑宇
》
售價：HK$
130.9
|
| 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
|
|
購物車/收銀台(0) | 在線留言板
| 付款方式
| 運費計算
| 聯絡我們
| 幫助中心 |
加入書簽
HOME
新書上架
