IP-内射环的扩张与IP-拟内射模  

The Extension of IP-Injective Rings and the IP-Quasi-Injective Modules

作　　者：王云霞[1] 陈建龙[2] 

机构地区：[1]河海大学理学院,江苏南京210098 [2]东南大学数学系,江苏南京210096

出　　处：《长春工业大学学报》2004年第3期13-16,共4页Journal of Changchun University of Technology

摘　　要：研究了IP 内射环的扩张,证明了:(1)若R是右IP 内射环,且满足ReR=R,其中e=e2∈R,则eRe是右IP 内射环;(2)给出了n阶矩阵环Mn(R)是右IP 内射环的两个等价刻画。同时,还将右IP 内射环推广到右IP 拟内射模,并证明了右IP 拟内射模一定是右F 拟内射模。The extensions of IP-injective rings are discussed. It is shown that:(1) if R is the right IP-injective ring with ReR=R, where e=e^2∈R, then eRe is a right IP-injective ring;(2) two equivalent characterizations of right IP-injective rings are given. In addtion, IP-injective rings are generalized to IP-quasi-injective modules and it is proven that a right IP-quasi-injective module, must be a right F-quasi-injective module.

关 键 词：矩阵环 IP-内射环 IP-拟内射模 F-拟内射模 

分 类 号：O153.3[理学—数学]