Подлинная книга Алгебра (3 -е издание) (Essence) Serge Lang World Book Publishing Company
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- Заголовок:Алгебра (3 -е издание) (нормально)
- Автор:Serge Lang
- Письмо,:Перевод Сержа Ланга
- Фрагментация:Твердая обложка
- Цены:126.0
- ISBN:9787506271844
- Издательство:World Book Publishing Company
- формат:24 Открыто
- Время печати:2007-10-01
- Версия:1
- Опубликованная дата:2007-10-01
- Количество страниц:914
- Внешний номер:9787506271844
PartOneTheBasicObjectsofAlgebra
ChapterIGroups
1.Monoids3
2.Groups7
3.Normalsubgr*ups*3
4.Cyclicgroups23
5.Operationsofagrouponaset25
6.Sylowsubgroups33
7.Directsumsandfreeabeliangroups36
8.Finitelygeneratedabeliangroups42
9.Thedualgroup46
10.Inverselimitandcompletion49
11.Categoriesandfunctors53
12.Freegroups66
ChapterIIRings
1.Ringsandhomomorphisms83
2.Commutativerings92
3.Polynomialsandgrouprings97
4.Localization107
5.Principalandfactorialrings111
ChapterIIIModules
1.Basicdefinitions117
2.Thegroupofhomomorphisms122
3.Directproductsandsumsofmodules127
4.Freemodules135
5.Vectorspaces139
6.Thedualspaceanddualmodule142
7.Modulesoverprincipalrings146
8.Euler-Poincar6maps155
9.Thesnakelemma157
~10.Directandinverselimits159
ChapterIVPolynomials
1.Basicpropertiesforpolynomialsinonevariable173
2.Polynomialsoverafactorialring180
3.Criteriaforirreducibility183
4.Hilbert'stheorem186
5.Partialfractions187
6.Symmetricpolynomials190
7.Mason-Stotherstheoremandtheabcconjecture194
8.Theresultant199
9.Powerseries205
PartTwoAlgebraicEquations
ChapterVAlgebraicExtensions
1.Finiteandalgebraicextensions225
2.Algebraicclosure229
3.Splittingfieldsandnormalextensions236
4.Separableextensions239
5.Finitefields244
6.Inseparableextensions247
ChapterVIGaloisTheory
1.Galoisextensions261
2.Examplesandapplications269
3.Rootsofunity276
4.Linearindependenceofcharacters282
5.Thenormandtrace284
6.Cyclicextensions288
7.Solvableandradicalextensions291
8.AbelianKummertheory293
9.TheequationXn-a=0297
10.Galoiscohomology302
11.Non-abelianKummerextensions304
12.Algebraicindependenceofhomomorphisms308
13.Thenormalbasistheorem312
14.InfiniteGaloisextensions313
15.Themodularconnection315
ChapterVIIExtensionsofRings
1.Integralringextensions333
2.IntegralGaloisextensions340
3.Extensionofhomomorphisms346
ChapterVIIITranscendentalExtensions
1.Transcendencebases355
2.Noethernormalizationtheorem357
3.Linearlydisjointextensions360
4.Separableandregularextensions363
5.Derivations368
ChapterIXAlgebraicSpaces
1.Hilbert'sNullstellensatz377
2.Algebraicsets,spacesandvarieties381
3.Projectionsandelimination388
4.Resultantsystems401
5.Specofaring405
ChapterXNoetherianRingsandModules
1.Basiccriteria413
2.Associatedprimes416
3.Primarydecomposition421
4.Nakayama'slemma424
5.Filteredandgradedmodules426
6.TheHilbertpolynomial431
7.Indecomposablemodules439
ChapterXIRealFields
1.Orderedfields449
2.Realfields451
3.Realzerosandhomomorphisms457
ChapterXIIAbsoluteValues
1.Definitions,dependence,andindependence465
2.Completions468
3.Finiteextensions476
4.Valuations480
5.Completionsandvaluations486
6.,Discretevaluations487
7.Zerosofpolynomialsincompletefields491
PartThreeLinearAlgebraandRepresentations
ChapterXIIIMatricesandLinearMaps
1.Matrices503
2.Therankofamatrix506
3.Matricesandlinearmaps507
4.Determinants511
5.Duality522
6.Matricesandbilinearforms527
7.Sesquilinearduality531
8.ThesimplicityofSL2(F)/±1536
9. TheGroupSln (F), n≥3540
ChapterXIVRepresentationofOneEndomorphism
1.Representations553
2.Decompositionoveroneendomorphism556
3.Thecharacteristicpolynomial561
ChapterXVStructureofBilinearForms
1.Preliminaries,orthogonalsums571
2.Quadraticmaps574
3.Symmetricforms,orthogonalbases575
4.Symmetricformsoverorderedfields577
5.Hermitianforms579
6.Thespectraltheorem(hermitiancase)581
7.Thespectraltheorem(symmetriccase)584
8.Alternatingforms586
9.ThePfaffian588
10.Witt'stheorem589
11.TheWittgroup594
ChapterXVITheTensorProduct
1.Tensorproduct601
2.Basicproperties607
3.Flatmodules612
4.Extensionofthebase623
5.Somefunctorialisomorphisms625
6.Tensorproductofalgebras629
7.Thetensoralgebraofamodule632
8.Symmetricproducts635
ChapterXVIISemisimplicity
1.Matricesandlinearmapsovernon-commutativerings641
2.Conditionsdefiningsemisimplicity645
3.Thedensitytheorem646
4.Semisimplerings651
5.Simplerings654
6.TheJacobsonradical,basechange,andtensorproducts657
7.Balancedmodules660
ChapterXVIIIRepresentationsofFiniteGroups
1.Representationsandsemisimplicity663
2.Characters667
3.1-dimensionalrepresentations671
4.Thespaceofclassfunctions673
5.Orthogonalityrelations677
6.Inducedcharacters686
7.Inducedrepresentations688
8.Positivedecompositionoftheregularcharacter699
9.Supersolvablegroups702
10.Brauer'stheorem704
11.Fieldofdefinitionofarepresentation710
12.Example:GL2overafinitefield712
ChapterXIXTheAlternatingProduct
1.Definitionandbasicproperties731
2.Fittingideals738
3.Universalderivationsandthe*e*ha*complex746
4.TheCliffordalgebra749
PartFourHomologicalAlgebra
ChapterXXGeneralHomologyTheory
1.Complexes761
2.Homologysequence767
3.EulercharacteristicandtheGrothendieckgroup769
4.Injectivemodules782
5.Homotopiesofmorphismsofcomplexes787
6.Derivedfunctors790
7.Delta-functors799
8.Bifunctors806
9.Spectralsequences814
ChapterXXIFiniteFreeResolutions
1.Specialcomplexes835
2.Finitefreeresolutions839
3,Unimodularpolynomialvectors846
4.TheKoszulcomplex850
Приложение1TheTrandendenceFaind π
Appendix2SomeSetTheory
Bibliography
Index
