Goldie extending modules and generalizations of quasi-continuous modules

Abstract

A module M is said to be quasi-continuous if it is extending with the condition (C₃) (cf. [7], [10]). In this paper, by using the notion of a G-extending module which is defined by E. Akalan, G. F. Birkenmeier and A. Tercan [1], we introduce a generalization of quasi-continuous “a GQC (generalized quasicontinuous)-module” and investigate some properties of GQC-modules. Initially we give some properties of a relative ejectivity which is useful in analyzing the structure of G-extending modules and GQC-modules (cf. [1]). And we apply them to the study of direct sums of GQC-modules. We also prove that any direct summand of a GQC-module with the finite internal exchange property is GQC. Moreover, we show that a module M is G-extending modules with (C₃) if and only if it is GQC-module with the finite internal exchange property.