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ID:39132504
大小:1.28 MB
页数:46页
时间:2019-06-25
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1、Generalizedlocalcohomologymodulesandlocalcohomologymoduleswithrespectto···AbstractAbstractLocalcohomologytheorygivenbyA.Grothendieckisanimportantcohomologytheory.Itisalsoallanimportantdirectionincommutativealgebra.Manymathematicianshavestudieditandhavemadeitwelldeveloped.In
2、1974,GermanymathematicianJ.Herzogdefinedgeneralizedlocalcohomologymodulesasageneralizationofusuallocalcohomologymodules.Inagradedring,wehaveknownthattheusuallocalcohomologymodulesandgeneralizedlocalcohomologymodulesbothhavethenaturalgradedstructures.In2007,R.Talmhashi,Y.Yos
3、hino,T.Yoshizawadefinedlocalcohomologymoduleswithrespecttoapairofideals(J,J)撼ageneralizationofusuallocalcohomologymodules.Inthispaper,wemainlystudygeneralizedlocalcohomologymodules,gradedgeneralizedlocalcohomologymodulesandlocalcohomologymoduleswithrespecttoapairofideals(I,
4、刀.Takingthespecialsituationsinsomeofourresults,wecangetsomeresultsforusuallocalcohomologymodules.Wedividethispaperintofivechapters.Themaincontentofthepaperisthefollowing:Inchapter1,werecallsomebasicconcepts,preliminaryresultsandsomefamoustheo-feints,whichwillbeprobablyusedi
5、nthispaper.Inchapter2,wemmnlystudytheweaklylaskerianproperti.es,weaklycofmiteness,van-ishingproperties,attachedprimes,associatedprimesandcoassociatedprimesofgeneralizedlocalcohomologymodules.Firstly,westudytherelationshipbetweentheweaklylaskerianpropertiesofH}(M,N)andthatof
6、啦(Ⅳ)andgetsomeequivalentconditionsoftheweaklylaskerianpropertiesofgeneralizedlocalcohomologymodules.Secondly,inalocalring(R,m),骶studysomepropertiesofaconstantquantityq(1,M,Ⅳ)=sup{i∈NoIH}(M,N)isnotm-weaklycofinite}.Afterdiscussing,wefindthatq(1,M,N)isbasedonS叩pR(Ⅳ).Thirdly,w
7、estudysomepropertiesofcd(I,M,N)=sup{/∈ⅣoIH}(M,N)≠o)andgetsomevanish-ingpropertiesofgeneralizedlocalcohomologymodules.Finally,westudytherelA.tioushipbetweentheattachedprimesandassociatedprimesofgeneralizedlocalcohomologymodulesanddiscussthefinitenesspropertiesofthecoassociat
8、edprimesofgeneralizedlocalcohomol-ogymodules.IIIGeneralizedlocalcohomologymodulesa
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