對模的根和基座的一些討論.pdf

1、四川師范大學(xué)碩士學(xué)位論文對模的根和基座的一些討論姓名：劉利平申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：汪明義20080301SomeStudiesontheRadicalsandSoclesofModulesWriter：LIULi—pingAbstract：Supervisor：WANGMingyiInthispaper，threepointsaxechieflydiscussedIWestudythepropertiesofradi

2、calsuperfluousmodules(RSmodulesforabbreviation)andsocleessentialrings，anddiscusstherelationshipbetweentheRSmoduleandBassmodulesAtthesametime，wedosomecharacterizationsonBassringandsemiartinianringIIWeintroducethenotionofs

3、ocprojectivemodulesandtadprojectivemodulesandstudytheequivalentcharacterizationsandpropertiesofSOCoprojectivemodulesandradprojectivemodulesInaddition，weuseSOCprojectivemodulestocharactersemisimplerings，PSrings，etc；weuser

4、adprojectivemadulestocharacterJsemisimplerings，etcAtlast，wegetaequalstatementonaSFringisaVonNemannregularringIIIWeintroducetheconceptofSOCflatmodulesandthehomologicaldimensionofSOC—flatmodules，andgetsomepropertiesofSOC—f

5、latmodulesandthehomologicaldimensionofSOCfiatmodulesAtlast，wegetageneralizationofChase’Stheorybysocflatmodules。Keywords：RSmodules；Bassrings；socleessentialrings；semisimplerings；PSrings；SOCprojectivemodules；radprojectivemo