抽象代数讲义（第3卷）

图书标准信息

• 作者 Nathan Jacobson 著
• 出版社 世界图书出版公司
• 出版时间 2000-12
• 版次 1
• ISBN 9787506200622
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 其他
• 页数 217页

【内容简介】

Thepresentvolumecompletestheseriesoftextsonalgebrawhichtheauthorbeganmorethantenyearsago.TheaccountoffieldtheoryandGaloistheorywhichwegivehereisbasedonthenotionsandresultsofgeneralalgebrawhichappearinourfirstvolumeandonthemoreelementarypartsofthesecondvolume，dealingwithlinearalgebra.ThelevelofthepresentworkisroughlythesameasthatofVolumeII.

【目录】

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

CHAPTERI￡oFINITEDIMENSIONALEXTENSIONFIELDS
1.Somevectorspacesassociatedwithmappingsoffields
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￡oGALOISTHEORYOFEQUATIONS
1.TheGaloisgroupofanequation
2.Pureequations
3.Galois'criterionforsolvabilitybyradicals
……