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1、TheMillenniumEditionStanleyBurrisH.P.SankappanavarACourseinUniversalAlgebraWith36IllustrationscS.BurrisandH.P.SankappanavarAllRightsReservedThisEditionmaybecopiedforpersonaluseThisbookisdedicatedtoourchildrenKuroshPhillipBurrisVeenaandGeetaandSanjaySankappanavarPrefacetotheMillenniumEditio
2、nTheoriginal1981editionofACourseinUniversalAlgebrahasnowbeenLaTeXedsotheauthorscouldmaketheout-of-printSpringer-VerlagGradu-ateTextsinMathematicseditionavailableonceagain,withcorrections.ThesubjectofUniversalAlgebrahasflourishedmightilysince1981,andwestillbelievethatACourseinUniversalAlgebr
3、aoersanexcellentintroductiontothesubject.SpecialthanksgotoLisD'AlessioforthesuperbjobofLaTeXingthisedition,andtoNSERCfortheirsupportwhichhasmadethisworkpossible.vAcknowledgmentsFirstwewouldliketoexpressgratitudetoourcolleagueswhohaveaddedsomuchvital-itytothesubjectofUniversalAlgebraduring
4、thepasttwentyyears.Oneoftheoriginalreasonsforwritingthisbookwastomakereadilyavailablethebeautifulworkonsheavesanddiscriminatorvarietieswhichwehadlearnedfrom,andlaterdevelopedwithH.Werner.Recentworkof,andwith,R.McKenzieonstructureanddecidabilitytheoryhasaddedtoourexcitement,andconviction,co
5、ncerningthedirectionsemphasizedinthisbook.InthelatestagesofpolishingthemanuscriptwereceivedvaluablesuggestionsfromM.Valeriote,W.Taylor,andthereviewerforSpringer-Verlag.Forhelpinproof-readingwealsothankA.Adamson,M.Albert,D.Higgs,H.Kommel,G.Krishnan,andH.Riedel.Agreatdealofcreditfortheexiste
6、nceofthenalproductgoestoSandyTamowskiwhoseenthusiastictypinghasbeenaconstantinspiration.TheNaturalSciencesandEngineeringResearchCouncilofCanadahasgenerouslyfundedboththeresearchwhichhasprovidedmuchoftheimpetusforwritingthisbookaswellasthepreparationofthemanuscriptthroughNSERCGrantNo.A7256
7、.AlsothanksgotothePureMathematicsDepartmentoftheUniversityofWaterloofortheirkindhospitalityduringtheseveralvisitsofthesecondauthor,andtotheInstituteofMathematics,FederalUniversityofBahia,fortheirgenerouscooperationinthisventure.Thesecondauthorwouldmostofalllik