bruns w., vetter u. determinantal rings(springer lnm 1327, 1988)(isbn 3540194681)(144s)

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1、LectureNotesinMathematics1327EditedbyA.DoldandB.EckmannWinfriedBrunsUdoVetterDeterminantalRingsSpringer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoAuthorsWinfriedBrunsFBMathematik/InformatikUniversit•atOsnabruc•k49069Osnabruc•kGermanyUdoVetterFBMathema

2、tikUniversit•atOldenburg26111OldenburgGermanyThisbookisnowoutofprint.TheauthorsaregratefultoSpringer-Verlagforthepermissiontomakethispostscriptleaccessible.ISBN3-540-19468-1Springer-VerlagBerlinHeidelbergNewYorkISBN0-387-19468-1Springer-VerlagNewYorkBer

3、linHeidelbergcSpringer-VerlagBerlinHeidelberg1988PrefaceDeterminantalringsandvarietieshavebeenacentraltopicofcommutativealgebraandalgebraicgeometry.Theirstudyhasattractedmanyprominentresearchersandhasmotivatedthecreationoftheorieswhichmaynowbeconsideredp

4、artofgeneralcommutativeringtheory.Acoherenttreatmentofdeterminantalringsislackinghowever.Wearealgebraists,andthereforethesubjectwillbetreatedfromanalgebraicpointofview.Ourmainapproachisviathetheoryofalgebraswithstraighteninglaw.Itsaxiomsconstituteaconven

5、ientsystematicframework,andthestandardmonomialtheoryonwhichitisbasedyieldscomputationallyeectiveresults.Thisapproachsuggests(andissimpliedby)thesimultaneoustreatmentofthecoordinateringsoftheSchubertsubvarietiesofGrassmannians,aprogramcarriedoutverystri

6、ctly.Othermethodshavenotbeenneglected.Principalradicalsystemsarediscussedindetail,andonesectioneachisdevotedtoinvariantandrepresentationtheory.However,freeresolutionsare(almost)onlycoveredfortheclassical"caseofmaximalminors.Ourpersonalviewofthesubjectis

7、mostvisiblyexpressedbytheinclusionofSections13{15inwhichwediscusslinearalgebraoverdeterminantalrings.InparticularthetechnicaldetailsofSection15(andperhapsonlythese)aresomewhatdemanding.Thebibliographycontainsseveraltitleswhichhavenotbeencitedinthetext.Th

8、eymainlycovertopicsnotdiscussed:geometricmethodsandidealsgeneratedbyminorsofsymmetricmatricesandPfaansofalternatingones.Wehavetriedhardtokeepthetextasself-containedaspossible.ThebasicsofcommutativealgebrasuppliedbyPartIof