ON GENERALIZED EXTENDING MODULES

被引：0

作者：

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

Sayed, A. ^{[1
]}

机构：

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

来源：

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE | 2007年 / 76卷 / 02期

关键词：

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：

H. Hanada, J. Kado, and K. Oshiro have introduced, in a diagram of modules and homomorphisms, the concept of generalized M-injective modules. S. Mohamed, and B. Mueller have given a different characterization, based on an exchange property, of the generalized M-injective modules. Here we introduce the concept of M-jective modules, which is a generalization of Mohamed and Mueller concept for the generalized M-injectivity. The concept of M-jective modules is used here to solve the problem of finding a necessary and sufficient condition for a direct sum of extending modules to be extending. In fact, we show that relative jectivity is necessary and sufficient for a direct sum of two extending modules to be extending. We also introduced the concept of generalized extending modules, and give some properties of such modules in analougy with the known properties for extending modules.

引用

页码：193 / 200

页数：8