Some Notes on Quasi AP-injective Modules  

作　　者：赵玉娥 杜先能 

机构地区：[1]School of Mathematical Sciences of Qingdao University,Qingdao,266071 [2]School of Mathematics and Computational Science of Anhui University,Hefei,230039

出　　处：《Northeastern Mathematical Journal》2006年第4期433-440,共8页东北数学（英文版）

基　　金：The NNSF(10371101 and 10371061)of China

摘　　要：Let R be a ring. A right R-module M with S = End（MR） is called a quasi AP-injective module, if, for any s C S, there exists a left ideal Xs of S such that ls（ker s） = Ss＋Xs. Let M be a quasi AP-injective module which is a self-generator. We show that for such a module, if S is semiprime, then every maximal kernel of S is a direct summand of M. Furthermore, if ker（a1） lohtain in ker（a2a1） lohtain in ker（a3a2a1） lohtain in... satisfy the ascending conditions for any sequence al, a2, a3,… ∈ S, then S is right perfect. In this paper, we give a series of results which extend and generalize results on AP-injective rings.Let R be a ring. A right R-module M with S = End（MR） is called a quasi AP-injective module, if, for any s C S, there exists a left ideal Xs of S such that ls（ker s） = Ss＋Xs. Let M be a quasi AP-injective module which is a self-generator. We show that for such a module, if S is semiprime, then every maximal kernel of S is a direct summand of M. Furthermore, if ker（a1） lohtain in ker（a2a1） lohtain in ker（a3a2a1） lohtain in... satisfy the ascending conditions for any sequence al, a2, a3,… ∈ S, then S is right perfect. In this paper, we give a series of results which extend and generalize results on AP-injective rings.

关 键 词：quasi AP-injective module AP-injective ring self-generator 

分 类 号：O153.3[理学—数学]