Let R be a ring. R is called right AP-injective if, for any a E R, there exists a left ideal of R such that lr（a） = Ra＋Xa. We extend this notion to modules. A right R-module M with S = End（MR） is called quasi AP-...Let R be a ring. R is called right AP-injective if, for any a E R, there exists a left ideal of R such that lr（a） = Ra＋Xa. We extend this notion to modules. A right R-module M with S = End（MR） is called quasi AP-injective if, for any s∈S, there exists a left ideal Xs of S such that ls（Ker（s）） = Ss＋Xs. In this paper, we give some characterizations and properties of quasi AP-injective modules which generalize results of Page and Zhou.展开更多
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 w...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.展开更多
文摘Let R be a ring. R is called right AP-injective if, for any a E R, there exists a left ideal of R such that lr（a） = Ra＋Xa. We extend this notion to modules. A right R-module M with S = End（MR） is called quasi AP-injective if, for any s∈S, there exists a left ideal Xs of S such that ls（Ker（s）） = Ss＋Xs. In this paper, we give some characterizations and properties of quasi AP-injective modules which generalize results of Page and Zhou.
文摘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.
