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经典英文数学教材系列:代数学(第1卷)(英文版)》特色:抽象与具体结合,理论与应用结合。目前的代数书,常常单线地朝抽象方向发展,使读者--甚至一些数学家们--觉得代数学是抽象概念的游戏。各种数学理论的平行发展,到了代数学中,取得了整合与统一。

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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