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1、TheMillenniumEditionStanleyBurrisH.P.SankappanavarACourseinUniversalAlgebraWith36IllustrationscS.BurrisandH.P.SankappanavarAllRightsReservedThisEditionmaybecopiedforpersonaluseThisbookisdedicatedtoourchildrenKuroshPhillipBurrisVeenaandGeetaandSanjaySankappanavarPrefacetotheMi
2、llenniumEditionTheoriginal1981editionofACourseinUniversalAlgebrahasnowbeenLaTeXedsotheauthorscouldmaketheout-of-printSpringer-VerlagGradu-ateTextsinMathematicseditionavailableonceagain,withcorrections.ThesubjectofUniversalAlgebrahasflourishedmightilysince1981,andwestillbelieve
3、thatACourseinUniversalAlgebrao ersanexcellentintroductiontothesubject.SpecialthanksgotoLisD'AlessioforthesuperbjobofLaTeXingthisedition,andtoNSERCfortheirsupportwhichhasmadethisworkpossible.vAcknowledgmentsFirstwewouldliketoexpressgratitudetoourcolleagueswhohaveaddedsomuchvit
4、al-itytothesubjectofUniversalAlgebraduringthepasttwentyyears.Oneoftheoriginalreasonsforwritingthisbookwastomakereadilyavailablethebeautifulworkonsheavesanddiscriminatorvarietieswhichwehadlearnedfrom,andlaterdevelopedwithH.Werner.Recentworkof,andwith,R.McKenzieonstructureandde
5、cidabilitytheoryhasaddedtoourexcitement,andconviction,concerningthedirectionsemphasizedinthisbook.InthelatestagesofpolishingthemanuscriptwereceivedvaluablesuggestionsfromM.Valeriote,W.Taylor,andthereviewerforSpringer-Verlag.Forhelpinproof-readingwealsothankA.Adamson,M.Albert,
6、D.Higgs,H.Kommel,G.Krishnan,andH.Riedel.Agreatdealofcreditfortheexistenceofthe nalproductgoestoSandyTamowskiwhoseenthusiastictypinghasbeenaconstantinspiration.TheNaturalSciencesandEngineeringResearchCouncilofCanadahasgenerouslyfundedboththeresearchwhichhasprovidedmuchoftheimp
7、etusforwritingthisbookaswellasthepreparationofthemanuscriptthroughNSERCGrantNo.A7256.AlsothanksgotothePureMathematicsDepartmentoftheUniversityofWaterloofortheirkindhospitalityduringtheseveralvisitsofthesecondauthor,andtotheInstituteofMathematics,FederalUniversityofBahia,forth
8、eirgenerouscooperationinthisventure.Thesecondauthorwouldmostofalllik
