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1、GeorgeGrätzerLatticeTheory:FoundationGeorgeGrätzerDepartmentofMathematicsUniversityofManitobaWinnipeg,ManitobaR3T2N2Canadagratzer@me.com2010MathematicsSubjectClassification06-01,06-02ISBN978-3-0348-0017-4e-ISBN978-3-0348-0018-1DOI10.1007/978-3-0348-0018-1LibraryofCongressControlNumber:
2、2011921250©SpringerBaselAG2011Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightoftranslation,reprinting,re-useofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinotherways,andstorageindatabanks.Foranykin
3、dofuse,permissionofthecopyrightownermustbeobtained.Coverdesign:deblik,BerlinPrintedonacid-freepaperSpringerBaselAGispartofSpringerScience+BusinessMediawww.birkhauser-science.comToCherylandDavid,forthesupporttheygaveme,whenitwasmostneeded...ShortContentsPrefacexviiForewordxixGlossaryofN
4、otationxxiiiIFirstConcepts11TwoDe nitionsofLattices12HowtoDescribeLattices213SomeBasicConcepts284Terms,Identities,andInequalities665FreeLattices756SpecialElements97IIDistributiveLattices1091CharacterizationandRepresentationTheorems1092TermsandFreeness1263CongruenceRelations1384BooleanA
5、lgebrasR-generatedbyDistributiveLattices1495TopologicalRepresentation1666Pseudocomplementation191IIICongruences2071CongruenceSpreading2072Distributive,Standard,andNeutralElements2233Distributive,Standard,andNeutralIdeals2344StructureTheorems244viiviiiContentsIVLatticeConstructions2551A
6、ddinganElement2552Gluing2623ChoppedLattices2694ConstructingLatticeswithGivenCongruenceLattices2765BooleanTriples294VModularandSemimodularLattices3071ModularLattices3072SemimodularLattices3293GeometricLattices3424PartitionLattices3595ComplementedModularLattices373VIVarietiesofLattices40
7、91CharacterizationsofVarieties4092TheLatticeofVarietiesofLattices4233FindingEquationalBases4384TheAmalgamationProperty454VIIFreeProducts4671FreeProductsofLattices4672TheStructureofFreeLattices4933ReducedFreeProducts5084Hop anLattices526Afterword533Bibliography539Index589ContentsPrefa
