Diyala Journal for Pure Science DJPS

P- ISSN:2222-8373, E-ISSN:2518-9255

Volume 16, Issue 1 , January  2020

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

Hana I. Lafta

Year: 2020, Volume: 16, Issue: 1

Pages: 37-44 , DOI: https://dx.doi.org/10.24237/djps.16.01.508A 

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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.

Keywords: Hollow-Quasi Module, Hollow Lifting-Discrete Module, Hollow-Lifting Module and Hollow-Lifting Quasi.