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1、TheMillenniumEditionStanleyBurrisH.P.SankappanavarACourseinUniversalAlgebraWith36IllustrationscS.BurrisandH.P.SankappanavarAllRightsReservedThisEditionmaybecopiedforpersonaluseThisbookisdedicatedtoourchildrenKuroshPhillipBurrisVeenaandGeetaandSanjaySankappanavarPrefaceto
2、theMillenniumEditionTheoriginal1981editionofACourseinUniversalAlgebrahasnowbeenLaTeXedsotheauthorscouldmaketheout-of-printSpringer-VerlagGradu-ateTextsinMathematicseditionavailableonceagain,withcorrections.ThesubjectofUniversalAlgebrahasflourishedmightilysince1981,andwest
3、illbelievethatACourseinUniversalAlgebrao ersanexcellentintroductiontothesubject.SpecialthanksgotoLisD'AlessioforthesuperbjobofLaTeXingthisedition,andtoNSERCfortheirsupportwhichhasmadethisworkpossible.vAcknowledgmentsFirstwewouldliketoexpressgratitudetoourcolleagueswhohav
4、eaddedsomuchvital-itytothesubjectofUniversalAlgebraduringthepasttwentyyears.Oneoftheoriginalreasonsforwritingthisbookwastomakereadilyavailablethebeautifulworkonsheavesanddiscriminatorvarietieswhichwehadlearnedfrom,andlaterdevelopedwithH.Werner.Recentworkof,andwith,R.McKe
5、nzieonstructureanddecidabilitytheoryhasaddedtoourexcitement,andconviction,concerningthedirectionsemphasizedinthisbook.InthelatestagesofpolishingthemanuscriptwereceivedvaluablesuggestionsfromM.Valeriote,W.Taylor,andthereviewerforSpringer-Verlag.Forhelpinproof-readingweals
6、othankA.Adamson,M.Albert,D.Higgs,H.Kommel,G.Krishnan,andH.Riedel.Agreatdealofcreditfortheexistenceofthe nalproductgoestoSandyTamowskiwhoseenthusiastictypinghasbeenaconstantinspiration.TheNaturalSciencesandEngineeringResearchCouncilofCanadahasgenerouslyfundedboththeresear
7、chwhichhasprovidedmuchoftheimpetusforwritingthisbookaswellasthepreparationofthemanuscriptthroughNSERCGrantNo.A7256.AlsothanksgotothePureMathematicsDepartmentoftheUniversityofWaterloofortheirkindhospitalityduringtheseveralvisitsofthesecondauthor,andtotheInstituteofMathema
8、tics,FederalUniversityofBahia,fortheirgenerouscooperationinthisventure.Thesecondauthorwouldmostofalllik
