群上環(huán)上可分函子若干性質(zhì)的研究.pdf

1、曲阜師范大學碩士學位論文群上環(huán)上可分函子若干性質(zhì)的研究姓名：于梅申請學位級別：碩士專業(yè)：基礎(chǔ)數(shù)學指導教師：王頂國20080401曲阜師范大學碩士學位論文AbstractLet￡=(厶)Q∈GbeaG—ACoring，whereAisaringwithunit，andGisagroupTheunitelementofGwillbedenotedbyeIn，thereistheconceptionofagroupcoringAndtheau

2、thorcangivethetensorproductofthecoringsandshowthatbicomodulesareinfactcomodulesIn，foranA—coringC，theauthorstudywhentwofunctors，theforgetfulfunctor：Mc_A4^andinductionfunctor—oC：MA_朋careseparableThispaperwantstoshowthatwhe

3、ntheforgetfulfunctor：M￡jMAAnditsrightadjointfunctorareseparableInsection3，wedefineabicomdulecM望，where￡isaG—Acoringand旦isaG—B—coringWealsoshowthatthebicomodulesareinfactcomodulesInsection4，weprovethatthereisapairofadjoint

4、functor(F4，G4)betweenthecategoriesM￡andMJ4Thenweprovethetwomainresultsofthispaper：Theorem45Let晝beacofreegroupcoring，andGisfiniteThenthefunctor0口∈G％(一oACe)isseparableifandonlyifthereexistsaninvarint—q=(qo)口6G∈￡^=go∈厶I％a=n

5、qa，Q∈Gsuchthate(qe)=1Theorem48LetG—A—coringbeacofreegroupcoring，andGisfiniteThentheforgetfulfunctorF：Mc人／f^isseparableifandonlyifthereexistsan丁∈HomA(o。∈G％(CepACe)，A)，suchthat7o(∑。∈Gi。o％oAe，e)=E，andcoe)7(0％(c(2。)。Ac7))=丁(