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时间:2020-06-20
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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
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