交换代数 第1卷

作者Oscar
出版社
出版时间2003-01-01

特色:

Thisbookisthechildofanunbornparent.SomeyearsagotheseniorauthorbeganthepreparationofaColloquiumvolumeonalgebraicgeometry,andhewasthenfacedwiththedifficulttaskofincorporatinginthatvolumethevastamountofpurelyalgebraicmaterialwhichisneededinabstractalgebraicgeometry.Theoriginal.planwastoinsert,fromtimetotime,algebraicdigressionsinwhichconceptsandresultsfromcommutativealgebraweretobedevelopedinfullasandwhentheywereneeded.However,itsoonbecameapparentthatsuchaparentheticaltreatmentofthepurelyalgebraictopics,coveringawiderangeofcommutativealgebra,wouldimposeartificialboundsonthemanner,depth,anddegreeofgeneralitywithwhichthesetopicscouldbetreated.Asiswellknown,abstractalgebraicgeometryhasbeenrecentlynotonlythemainfieldofapplicationsofcommutativealgebrabutalsotheprincipalincentiveofnewresearchincommutativealgebra.Toapproachtheunderlyingalgebraonlyinastrictlyutilitarian,auxiliary,andparentheticalmanner,tostopshortofgoingfurtherafieldwheretheapplicationsofalgebratoalgebraicgeometrystopandthegeneralalgebraictheoriesinspiredBygeometrybegin,impressedusincreasinglyasbeingaprogramscientificallytoonarrowandpsychologicallyfrustrating,nottomentionthedistractingeffectthatrepeatedalgebraicdigressionswouldinevitablyhavehadonthereader,vis-h-visthecentralalgebro-geometrlctheme.Thustheideaofaseparatebookoncommutativealgebrawasborn,andthepresentbook--ofwhichthisisthefirstoftwovolumes--isarealizationofthisidea,cometofruitionatatimewhenitsparent--atreatiseonabstractalgebraicgeometry-hasstilltoseethelightoftheday.

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