ON n-VNL-modules and SVNL-modules

Journal: Region - Educational Research and Reviews DOI: 10.32629/rerr.v2i4.219

Le Cheng, Hui Wang

Department of Mathmatics and Computer Science, HeTao College

Abstract

A ring R is called right n-VNL-ring if whenever a1R+a2R+...+anR=R for some elements a1,a2,...an∈R, there exists at least one element  ai regular. The aim of this paper is to generalize this concept into module classes, we define n-VNL-modules, study their properties and give some characterizations. It is proved that for any finite generated R- module M, M is an SVNL-module if and only if M is an n-VNL-module for every positive integer n. The locally projective n-VNL-modules are also be characterized. We discuss the relationship between n-VNL-modules and other modules under different conditions.

Keywords

n-VNL-ring; n-VNL-module; SVNL-ring; SVNL-module

Funding

This research was supported by the Natural Science Foundations of HeTao College (HYZQ201945): Research on Generalization and Application of VNL Rings.

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Copyright © 2020 Le Cheng, Hui Wang

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