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| 內容簡介： |
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ThepresentvolumeisthefirstofthreethatwillbepublishedunderthegeneraltitleLecturesinAbstractAlgebra.Thesevol-umesarebasedonlectureswhichtheauthorhasgi，renduringthepasttenyearsattheUniversityofNorthCarolina，atTheJohnsHopkinsUniversity，andatYaleUniversity.Thegeneralplanoftheworkisasfollows:Thepresentfirstvolumegivesanintroductiontoabstractalgebraandgivesanaccountofmostoftheimportantalgebraicconcepts.Inatreatmentofthistypeitisimpossibletogiveacomprehensiveaccountofthetopicswhichareintroduced.Neverthelesswehavetriedtogobeyondthefoundationsandelementarypropertiesofthealgebraicsys-tems.Thishasnecessitatedacertainamountofselectionandomission.Wefeelthatevenatthepresentstageadeeperunder-standingofafewtopicsistobepreferredtoasuperficialunder-standingofmany.
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| 目錄：
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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
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