相对半遗传环与半遗传环  

Relative Semi-hereditary Rings and Semi-hereditary Rings

作　　者：班秀和[1] 

机构地区：[1]广西师范学院数学与计算机科学系,广西南宁530001

出　　处：《湖南文理学院学报（自然科学版）》2007年第4期25-26,53,共3页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：广西科学基金(0575052;0640070)

摘　　要：用余平坦模和M-半遗传环刻画了半遗传环,得到:R是半遗传环,当且仅当E(R)的商是余平坦模,当且仅当R是R-半遗传环,当且仅当每个模的任意两个同构内射子模的和是余平坦模.还用余平坦模刻画了QF-环和正则环,证明了:R为QF-环,当且仅当余平坦模是投射模,当且仅当投射模是余平坦模且R是Noether环;R为正则环当且仅当R的每个循环左理想余平坦.Using coflat modules and M-semi-hereditary rings, it is obtained that R is a semi- hereditary ring iff the factors of E(R) is coflat iff R is a R-semi-hereditary ring iff the sum of two injective submodules in a module that are isomorphic is coflat.Then, by coflat modules the following results are shown: R is a QF- ring iff coflat modules are projective iff projective modules are coflat and R is a Noetherian ring;R is a regular ring iff every cyclic left ideal in R is coflat.

关 键 词：余平坦模 M-半遗传环 半遗传环 QF-环 正则环 

分 类 号：O153.3[理学—数学]