抽象代数讲义（第1卷）（英文）

图书标准信息

• 作者 [德]雅格布斯（Jacobson N.） 著
• 出版社 世界图书出版公司
• 出版时间 2013-10
• 版次 1
• ISBN 9787510061516
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 217页
• 正文语种 英语

【内容简介】

　　ThepresentvolumeisthefirstofthreethatwillbepublishedunderthegeneraltitleLecturesinAbstractAlgebra.Thesevol-umesarebasedonlectureswhichtheauthorhasgi，renduringthepasttenyearsattheUniversityofNorthCarolina，atTheJohnsHopkinsUniversity，andatYaleUniversity.Thegeneralplanoftheworkisasfollows:Thepresentfirstvolumegivesanintroductiontoabstractalgebraandgivesanaccountofmostoftheimportantalgebraicconcepts.Inatreatmentofthistypeitisimpossibletogiveacomprehensiveaccountofthetopicswhichareintroduced.Neverthelesswehavetriedtogobeyondthefoundationsandelementarypropertiesofthealgebraicsys-tems.Thishasnecessitatedacertainamountofselectionandomission.Wefeelthatevenatthepresentstageadeeperunder-standingofafewtopicsistobepreferredtoasuperficialunder-standingofmany.

【目录】

INTRODUCTION:CONCEPTSFROMSETTHEORYTHESYSTEMOFNATURALNUMBERS
SECTION
1.Operationsonsets
2.Productsets,mappings
3.Equivalencerelations
4.Thenaturalnumbers
5.Thesystemofintegers
6.ThedivisionprocessinI

CHAPTERI:SEMI-GROUPSANDGROUPS
1.Definitionandexamplesofsemi-groups
2.Non-associativebinarycompositions
3.Generalizedassociativelaw.Powers
4.Commutativity
5.Identitiesandinverses
6.Definitionandexamplesofgroups
7.Subgroups
8.Isomorphism
9.Transformationgroups
10.Realizationofagroupasatransformationgroup
II.Cyclicgroups.Orderofanelement
12.Elementarypropertiesofpermutations
13.Cosetdecompositionsofagroup
14.Invariantsubgroupsandfactorgroups
15.Homomorphismofgroups
16.Thefundamentaltheoremofhomomorphismforgroups
17.Endomorphisms,automorphisms,centerofagroup
18.Conjugatcclasses

CHAPTERII:RINGS,INTEGRALDOMAINSANDFIELDS
SECTION
1.Definitionandexamples
2.Typesofrings
3.Quasi-regularity.Thecirclecomposition
4.Matrixrings
5.Quaternions
6.Subringsgeneratedbyasetofelements.Center
7.Ideals,differencerings
8.Idealsanddifferenceringsfortheringofintegers
9.Homomorphismofrings
10.Anti-isomorphism
11.Structureoftheadditivegroupofaring.Thecharateristicofaring
12.Algebraofsubgroupsoftheadditivegroupofaring.Onrsidedideals
13.Theringofendomorphismsofacommutativegroup
14.Themultiplicationsofaring

CHAPTERIII:EXTENSIONSOFRINGSANDFIELDS
1.Imbeddingofaringinaringwithanidentity
2.Fieldoffractionsofacommutativeintegraldomain
3.Uniquenessofthefieldoffractions
4.Polynomialrings
5.Structureofpolynomialrings
6.Propertiesofthering2l[x]
7.Simpleextensionsofafield
8.Structureofanyfield
9.Thenumberofrootsofa'polynomialinafield
10.Polynomialsinseveralelements
11.Symmetricpolynomials
12.Ringsoffunctions

CHAPTERIV:ELEMENTARYFACTORIZATlONTHEORY
1.Factors,associates,irreducibleelements
2.Gaussiansemi-groups
3.Greatestcommondivisors
4.Principalidealdomains
……

CHAPTERV:GROUPSWITHOPERATORS
CHAPTERVI:MODULESANDIDEALS
CHAPTERVII:LATTICES
Index