H-supplemented Modules and Generalizations of Quasi-discrete Modules

In this article, we introduce a generalization of quasi-discrete (a GQD-module) by using the notion of H-supplemented modules and investigate some properties of GQD-modules. First we consider some properties of a relative radical projectivity which is useful in analyzing the structure of H-supplemented modules. We apply them to the study of direct sums of GQD-modules. Moreover, we prove that any H-supplemented (lifting) module with finite internal exchange properly (FIEP) has an indecomposable decomposition and show that, for an H-supplemented (lifting) module, the finite exchange property implies the full exchange property.