On Some Properties of Hollow-Lifting-Quasi-Discrete Modules

Abstract

A notion of the Hollow-Lifting-Quasi-Discrete modules can constitute avery important situation in the module theory. In this paper we will present a key role in some properties and characterizations of Hollow-Lifting-Quasi-Discrete Modules, also we study characterization the relation between lifting property and Hollow-Lifting-Quasi-Discrete Modules. We introduced and study the concept of Hollow-Lifting-Quasi-Discrete Modules a generalization of Hollow-Quasi-Discrete Modules. In this work, we introduce and study classes of concepts which are extremities of Hollow-lifting-Quasi-Discrete modules. We call an R-module M Hollow-Lifting-Quasi-Discrete, if every submodule N of M with hollow-lifting module, there exists a stable direct summand K of M such that in M. we have the following proper implication:

Hollow-Lifting → Hollow-Lifting-Discrete → Hollow-Lifting-Quasi-Discrete Module.