新書推薦：
《
拉贝日记（全新版本。）
》
售價：HK$
96.8
《
情绪脑科学 ：解锁大脑密码，重获情绪自由
》
售價：HK$
53.9
《
超智能与未来：宇宙进化、科技趋势与人类未来
》
售價：HK$
85.8
《
人比AI凶（“中国好书”“文津图书奖”得主万维钢全新力作；当AI无所不能，你靠什么不可替代？答案就在这里！）
》
售價：HK$
86.9
《
鲶鱼之怒：日本大众文化中的天灾·疫病·怪异
》
售價：HK$
75.9
《
经典译林：罗生门
》
售價：HK$
42.9
《
现场：细读《史记》
》
售價：HK$
53.9
《
传奇与绝技：木拱桥里的中国营造智慧
》
售價：HK$
85.8
|
| 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
