关于拟P-内射模的一些注记(英文)

设 R是一个环 .一个右 R-模 M叫做拟 P-内射的 ,如果 M的每个 M-循环子模到 M的任一个 R-同态都能扩展到 M.假设 M是一个自生成子的拟 P-内射模 .在这篇文章中 ,我们表明如果这样一个模是一个 CF-模 (特别地 ,CS-模 ) ,那么 S/J(S)是正则的 ,其中 S=End(MR) .进一步 ,如果 S是半素环 ,那么 M的每个极大核是 M的一个直和项 .这些结果扩展了 P-内射环的一些结果

Some Notes on Quasi P-injective Modules

Let R be a ring. A right R-module M is called quasi P-injective module if every R-homomor-phism from an M-cyclic submodule of M to M can be extended to M. Let M be a quasi P-injective module whichis a self-generator. In this paper, we show that if such a module M is a CF-module (in particular, CS-module),then S/J(S) is regular, where S=End(MR). Further, if S is a semiprime ring, then every maximal kernel ofM is a direct summand of M. These results generalize the results on P-injective ring.