形式三角矩陣環(huán)上的模.pdf

1、東南大學碩士學位論文形式三角矩陣環(huán)上的模姓名：張小向申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：陳建龍2001.6.1Asweallknown，arightperfectringisarightMax—ring(ie，everynonzerorightmodulehasamaximalsubmodule)Itwasprovedin【12】thatTisarightperfectringifandonlyifbothAandBarerigh

2、tperfecttingsWeextendthisresulttothecaseofrightMax—ringsandshowthatTisarightMaxringifandonlyifbothAandBarefightMax—ringsWhereastheprojectivecoverwasinvestigatedin【12】，wecharacterizethesuperfluouscoverandessentialenvelope

3、of(Ⅳ，l，)，Attheendofchapter1，wecalculatethetraceandtherejectof(x，y)r，therebyimprovetheresultabouttheradicalandthesoeleof(z，，，)rin[12]Theprojectivityof(z，y)，hasbeencharacterizedin【12】，whilethefreenessandflatnessof(X，r)，hav

4、en’tbeenstudiedyetInchapter2，westudyfreemodulesovertheringsofMoritacontextsfirstThenapplytheresultgottenalreadytotheformaltriangularmatrixringTandsoIvetheproblemofcharacterizingthefreenessof(x，r)，completelyWeshowthatfora

5、nynonemptyset人，(Ⅳ，Y)，蘭T‘“’ifandonlyifⅣ^=(X／Im，)』蘭A㈥，％蘭B‘，and廠isamonomorphismInconsequence“wegettheresultontheprojectivityof(Ⅳ，’，)，in[121Asfortheflatnessof(Ⅳ，r)，，wegiveacriterionforitInaddition，wealsogetsomeresultsonthein