TS-模的有限直和.pdf

1、東北大學碩士學位論文TS模的有限直和姓名：吳穎林申請學位級別：碩士專業(yè)：基礎(chǔ)數(shù)學指導教師：樊復生2001.6.1幽!!!旦業(yè)墮幽墮!!!!型嬰盟一』幽墜￡LABSTRACTLetRbearingAclass鞏ofR—modulesiscalledanaturalclassifitisclosedundersubniodules，directsums，injectivehullsandisomorphiccopiesAsubmoduleN

2、ofMiscalledatypesubmoduleofMifNisamaximalelementinthecollectionofsubmodulesUofMwithU∈mforsomenaturalclassmAmoduleMiscalledaTS—moduleifeverytypesubmoduleofMisadirectsummandofMAnonzeromoduleMiscalledanatomicmoduleifanytwon

3、onzerosubmodulesofMcontaintwonon—zeroisomorphicsubmodulesAmoduleMiscalledoffinitetypedimensionn，ifMcontainsanessentialdirectsumof月pairwiseorthogonalatomicsubmodulesInChapter2ofthisthesis，weinvestigatewhendirectsumsoffini

4、telymanyCSmodulesareCS；theninChapter4weconcernaboutwhendirectsumsoffinitelymanyTSmodulesareTSandobtaintwomainresultsTheorem6(inChapter4)LetMMlo0肘bethedirectsumofr／pairwiseorthogonalrelativelyinjectivesubmodulesMj，i=1，，n，

5、of肘ThenMisTSiffallMareTSTheorem18(inChapter4)AmoduleMisaTSmodulewithfinitetypedimensioniff(a)Misafinitedirectsumofpairwiseorthogonalatomicsubmodules，and(b)everytypedirectsummandofMoftypedimension2isaTSmoduleWealsogiveall

6、alternativeproofofthefollowingresultTheorem15(inChapter∞LetMMl固固M。bethedirectsumofnpairwiseorthogonalrelativelyinjectivesubmodulesM，，i=Ip1F／，ofMThenMisaweakquasicontinuousmoduleiffallM，arerelativelyinjectiveweakquasi—con