ON P-EXTENDING MODULES

被引：0

作者：

Kamal, M. A. ^{[1
]}

Elmnophy, O. A. ^{[2
]}

机构：

[1] Ain Shams Univ, Dept Math, Fac Educ, Cairo, Egypt

[2] Ain Shams Univ, Fac Women, Dept Math, Cairo, Egypt

来源：

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE | 2005年 / 74卷 / 02期

关键词：

Principally injective modules; extending modules;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a ring. A right R-module M is called quasi-principally injective if it is M-principally injective. In this paper, we give some characterizations and properties of principally injective modules, which generalize results of Nicholson and Yousif. For a quasi-principally injective module M, we show: 1. For isomorphic submodules H, K of M, we have SH = SK, where S is the endomorphism ring of M. 2. M has (PC2), and consequently has (PC3). We characterize when a direct sum of P-extending modules is P-extending, and when a direct sum of a P-extending module and a semi-simple module is P-extending. We also characterize when a direct sum of FP-extending modules is FP-extending. Finally, we discuss when a direct sum of P-extending modules with relatively EC-injective is P-extending.

引用

页码：279 / 286

页数：8