Algebra, 代数学（第1卷）, 范德瓦尔登
代数入门读物，大师 经典好书， 现货 正文为英文。入门教材
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作者范德瓦尔登
出版社世界图书出版公司
ISBN9787506291606
出版时间2007-10
装帧平装
上书时间2024-05-07
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本书适合初次接触抽象代数的本科生，设计灵活，适合各种长度和不同复杂程度的抽象代数课程，从传统的抽象代数课程到更偏向应用的课程。这本书围绕两个主题展开：算术和一致性。每个主题都是先以整数为例，然后过渡到多项式，最后过渡到环和群，这样学生就可以看到这些抽象概念来自哪里，它们为什么很重要，以及它们之间的关联性。
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
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