广义局部上同调模和关于理想对（I，J）的局部上同调模

《广义局部上同调模和关于理想对（I，J）的局部上同调模》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

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