直内射模与扩张直内射模

Direct Injective Modules and Extending Direct Injectlve Modules

本文是关于直内射模工作的继续.文章首先进一步讨论了直内射模的性质,得到:一个环R是Artin半单环的充分必要条件是每个R-模都是直内射模.然后根据Harada关于模的扩张性的定义,研究了扩张直内射模,指出了当R-模M是扩张直内射模时,Krull-Schmidt-Matlis问题有肯定的回答.同时还证明了模的扩张直内射性按直和项保持.

This paper continues the author's work of the characterisation of direct injective modules. In this paper we study the properties of direct injective and extending direct injective modules, and obtain the following results: ①We esta- blish a necessary and sufficient condition for a ring be artinian s.misimple ring . ②We show that the answer to the problem of Krull-Schmidt-Matlis is affirmative in case R-module M is extending direct injective.③We prove that the extending direct injectivity of a module implies the same for its direct summands.