半对偶化对和半对偶化双模的一个刻画.pdf

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1、南京大学学报数学半年刊第31卷第1期JOURNALOFNAT、jJINGUNIVERSITYVo1．31，No．12014年5月MATHEMATICALBIQUARTERLYMay，2014DOI：10．3969／j．issn．0469—5097．2014．01．002SEMIDUALIZINGPAIRANDACHARACTERIZATIoN0FSEMIDUALIZINGBIMoDULESZhangZhen，GUOXiuhua，TaoLinlin(DepartmentofPrimaryEducation，ZiBoNormalCollege，255

2、100，ZiBoPRC)AbstractInthisnote，weintroduceandinvestigateasemidualizingpairoverallArtinalgebrawhichextendsthenotionoftiltingpairintroducedbyMiyashita．Weextendsomeconclusionsaboutsemidualizingmoduletosemidualizingpair．Ontheotherhand，wegiveacharacterizationofasemidualizingmodule

3、overanyassociativering．Keywordssemidualizingpair，tiltingmodule；Wakamatsutiltingmodule；selforthog。onalAMS(2000)subjectclassification16D20，16D90，16E05，16E10，16E300IntroductionThenotionofsemidualizingmoduleswasstudiedmorethan27yearsagounderothernamesby，e．g．，Foxby[al(PG—modulesof

4、rank1)，Golod[】(suitablem0dule8)andVascolcelos[。】(sphericalmodules)，whichcouldbeviewedasageneralizationofdualizingmodules·Relativealgebrawithrespecttoasemidualizingmodulehascaughtmanyauthors’atten-Received：2014-04—11；Revised：M『dy30，2014．E．mail：zhangzhebiye@gmail．corn；gxh607@si

5、na．corn10南京大学学报数学半年刊2014年5月tion．Forthistopic，wereferthereaderstoseeHolmandWhite’swork[7]，butalsotosee[6】j[10]，[11]，[12]．HolmandWhite[]extendedthenotionofsemidualizingmodulestotheasso—ciativering，wheretheydefinedthesemidualizing(S，R)bimodulesCnforanyassociativeringsRandS，(seeD

6、efinition1．7)．Ontheotherhand，theWakamatsutiltingmoduleisakindofgeneralizationofthetiltingmodule([，D。6“。“··1)，anditwasfirstintroducedbyWakamatsuin【14]．Notethattilt．ingmodulesin[15】areknownasWakamatsutiltingmodulesnow．AccordingtotheworkofWakamatsu[．wecandeducethatoveracommutati

7、veringR．asemidualizingR—moduleTisalwaysaWakamatsutiltingR—modulewithEndRT=R．However．aWakamatsutiltingR—moduleTisaleft．rightEndnT—semidualizingbimodulebutbyisnotasemidualizingR—bimoduleingenera1．InstudyingtiltingmodulesoverArtinalgebras．Miyashita[】introducedthenotionoftiltingp

8、air．Itisprovedthattiltingpairisageneralizationoftiltingmodule．Moreov