A GENERALIZATION OF g-SUPPLEMENTED MODULES

Kosar B., NEBİYEV C., Pekin A.

MISKOLC MATHEMATICAL NOTES, vol.20, no.1, pp.345-352, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.18514/mmn.2019.2586
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.345-352
  • Keywords: small submodules, radical, supplemented modules, radical (generalized) supplemented modules
  • Istanbul University Affiliated: Yes

Abstract

In this work g-radical supplemented modules are defined which generalize g-supplemented modules. Some properties of g-radical supplemented modules are investigated. It is proved that the finite sum of g-radical supplemented modules is g-radical supplemented. It is also proved that every factor module and every homomorphic image of a g-radical supplemented module is g-radical supplemented. Let R be a ring. Then R-R is g-radical supplemented if and only if every finitely generated R-module is g-radical supplemented. In the end of this work, it is given two examples for g-radical supplemented modules separating with g-supplemented modules.