presentvolumeisthefirstofthreethatwillbepublishedunderthegeneraltitleLecturesinAbstractAlgebra.Thesevol-umesarebasedonlectureswhichtheauthorhasgi,renduringthepasttenyearsattheUniversityofNorthCarolina,atTheJohnsHopkinsUniversity,andatYaleUniversity.ThegeneralplanoftheworkisasfollowsThepresentfirstvolumegivesanintroductiontoabstractalgebraandgivesanaccountofmostoftheimportantalgebraicconcepts.Inatreatmentofthistypeitisimpossibletogiveacomprehensiveaccountofthetopicswhichareintroduced.Neverthelesswehavetriedtogobeyondthefoundationsandelementarypropertiesofthealgebraicsys-tems.Thishasnecessitatedacertainamountofselectionandomission.Wefeelthatevenatthepresentstageadeeperunder-standingofafewtopicsistobepreferredtoasuperficialunder-standingofmany.
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