關(guān)于τ-n-凝聚環(huán).pdf

1、浙江師范大學(xué)碩士學(xué)位論文關(guān)于τn凝聚環(huán)姓名：朱海燕申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：陳淼森20040501AbstractCoherentringisoneofthemostimportantandintriguing8spectofringtheoryThemainthemeofthepaperwastostudyn—coherencerelativetoanarbitrary(hereditary)torsionth∞r(nóng)ie

2、s，andtoobtaincharacterizationSof1eft卜扎coherentringsfora丘XedpositiVeiⅡtegernWegaveVariousequi、，alentcoⅡditionsforaringtobe7一億一coherentMeanwhilewediscllssedthesomepmpertiesofr吼一coherentItwasshawnthattherearemanysimil壯ities

3、betweencoherentringsand7_一n—coherentrings，thensomeknownresult8oncoherentringswereobtaineda8coroIlaries，Thepaperconsistsofthreechapters，andinchapteroneweintroducedtherevelantbackgroundofcoherenceandthem缸ndirectionsincoher

4、enceresearchingInchaptert、∞，、Ⅳenotonlyde矗ned丁一禮_presentedmoduIes，butdsoprovedthatfora矗xedp08itiveintegernandr一(禮一1)一presentedmoduIeM，thenthefollowingsareequiVment(1)j“主Sr—n—presented(2)Ezt譬1(M，氈堊M)竺墮里EztFl(M，Ⅳt)，foreachd

5、irectsystemⅣt)oftorsionfreeR—modul8(3)T。r是I(Ⅳ，M)蘭E。巧f1(M，Ⅳ)，foreverytorsionfreem。duleⅣ。(4)丁。r是l(E，M)=o，foreachtor8ionfreeinjectivemoduleEThenwealsode6nedr—n—coherentmodules，7_一n—absolutelypuremodulesand丁一n—f越tmodukswhidl

6、werebasedon7一r卜presentedmodules，andweinVestigatedtherel舭ionshipbetween丁一mabs01utelypuremodulesand卜n—f越tmodulesAtlastwecharactenzeditintermsofrelativen—abs01utelypuremodulesandrelativenflatmodulesInchapterthree、vega^，ede矗

7、nitionsofu—dulemodules8sageneralizeddulemoduleandr—abs01utelypureresolutionsWbinvestigatedtheirpropertyon下一n—coherentrings，thenwegotthatproviedthatRisacommutativecoherentringandRRistorsionlessf—absoIutelypureRmodme，then距