代数学（第1卷）

图书标准信息

• 作者 [瑞士]范德瓦尔登 著
• 出版社 世界图书出版公司
• 出版时间 2007-10
• 版次 1
• ISBN 9787506291606
• 定价 35.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 265页

【内容简介】

The"abstract,""formal"or"axiomatic"direction,towhichthefreshimpetusinalgebraiseuc,hawled,hawledtoanumbeofnewformulationsofideas,insightintonewinterrelations,andfar-reachingresultsresults,especiallyingrouptheory,fieldtheory,valuationtheory,idealtheory,andthetheoryofhypercomplexnumbers.Theprincipalobjectiveofthisreason,genreralconceptsandmethodsstandintheforegorund,particularresultswhichproperlybelongtoclassicalalgebramustalsobegiveappropriateconsiderationwithintheframrworkofthemoderndevelopment.

【目录】

Chapter1NUMBERSANDSETS
1.1Sets
1.2Mappings,Cardinality
1.3TheNumbersequence
1.4Finiteandcountable(denumerable)sets
1.5partitions
Chapter2GROUPS
2.1Theconceptofagroup
2.2subgrougs
2.3compleses.cosets
2.4Isomorphismsandautomorphisms
2.5Homomorphisms,normalsubgroups,andfactorgroups
Chapter3RINGSANDFIELDS
3.1Rings
3.2HomomorphismandIsomorphism
3.3Theconceptofafieldquotients
3.4Polynomialrings
3.5Ideals,residueclassrings
3.6divesibility.primeideals
3.7Euclideanringsandprincipalidealrings
3.8Factorization
Chapter4VECTORSPACESANDTENSORSPACES
4.1Vectorspaces
4.2Dimensionalinvariance
4.3Thedualvectorspace
4.4Linearequationsinaskewfield
4.5Lineartransformations
4.6Tensors
4.7Antisymmetricmultilinearformsanddeterminants
4.8Tensorproducts,contraction,andtrace
Chapter5POLYNOMIALS
5.1Differentiation
5.2Thezerosofapolynomial
5.3Interpolationformulae
5.4Factorixation
5.5Irrdeucibilitycriteria
5.6Factorixationinafinitenumberofsteps
5.7symmetricfunctions
5.8theresultantoftwopolynomials
5.9theresultantasasymmetricfunctionoftheroots
5.10partialfractiondecomposition
Chapter6THEORYOFFIELDS
Chapter7CONTINUATIONOFGROUPTHEORY
Chapter8THEGALOILTHEEORY
Chapter9ORDERINGANDWELLORDERINGOFSETS
Chapter10INFINITEFIELDEXTENSIONS
Chapter11REALFIELDS
INDEX