新書推薦：
《
信息、生命与物理学
》
售價：HK$
90.9
《
士仕之间：汉代士人与政治
》
售價：HK$
78.2
《
Redis 高手心法
》
售價：HK$
115.0
《
勇往值钱：做自己人生的CEO
》
售價：HK$
68.8
《
里山资本主义：不做金钱的奴隶，做个安心的里山主人（献礼大地）
》
售價：HK$
67.9
《
欧洲雇佣兵研究（1350-1800）
》
售價：HK$
74.8
《
费里尼的电影
》
售價：HK$
102.4
《
第一性原理：21堂科学通识课（《奇怪的知识增加了》作者马库斯·乔恩全新力作）
》
售價：HK$
90.9
|
| 內容簡介： |
|
ThepresentvolumeisthefirstofthreethatwillbepublishedunderthegeneraltitleLecturesinAbstractAlgebra.Thesevol-umesarebasedonlectureswhichtheauthorhasgi，renduringthepasttenyearsattheUniversityofNorthCarolina，atTheJohnsHopkinsUniversity，andatYaleUniversity.Thegeneralplanoftheworkisasfollows:Thepresentfirstvolumegivesanintroductiontoabstractalgebraandgivesanaccountofmostoftheimportantalgebraicconcepts.Inatreatmentofthistypeitisimpossibletogiveacomprehensiveaccountofthetopicswhichareintroduced.Neverthelesswehavetriedtogobeyondthefoundationsandelementarypropertiesofthealgebraicsys-tems.Thishasnecessitatedacertainamountofselectionandomission.Wefeelthatevenatthepresentstageadeeperunder-standingofafewtopicsistobepreferredtoasuperficialunder-standingofmany.
|
| 目錄：
|
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
|
|
購物車/收銀台(
0
) | 在線留言板
| 付款方式
| 運費計算
| 聯絡我們
| 幫助中心 |
加入書簽
HOME
新書上架
