关于GP-内射环  

ON GP-INJECTIVE RINGS

作　　者：雷震[1] 

机构地区：[1]芜湖师范专科学校数学系,安徽芜湖241000

出　　处：《安徽师范大学学报（自然科学版）》2002年第2期112-114,共3页Journal of Anhui Normal University(Natural Science)

摘　　要：设R ,T为环 ,M是左R—右T-双模 ,且MTT忠实的 ,T是右GP—内射的当且仅当对任意t(≠ 0 ) ∈T ,存在非负整数n ,使tn ≠ 0 ,有Mtn =(Mtn) C) S,且Ttn =(Mtn:M ) T;T是左GP—内射的当且仅当对任意t(≠ 0 ) ∈T ,存在非负整数使tn ≠ 0 .有tnT =rTlM(tn)且lM(tn)=((lM(tn) ) S) .Let R and T be two rings,let M be a left R-right T-bimodule and M T be faithful.In the paper,we study the GP-injectivity of T by  RM T. The main results are the following:(1)T is a right GP-injective ring if and only if for any t(≠0)∈T,there exists a positive integer n with t n≠0,such that Mt n((Mt n) C) S,and Tt n(Mt n∶M) T;(2) T is s left GP-injective ring if and only if for any t(≠0)∈T,there exists a positive integer n with t n≠0,such that t nT=r Tl M(t n) and l M(t n)=((l M(t n)) S).

关 键 词：GP-内射环 P-内射环 忠实模 

分 类 号：O153.3[理学—数学]