ESSENTIAL G-RADICAL SUPPLEMENTED MODULES


Nebiyev C., Okten H. H.

MISKOLC MATHEMATICAL NOTES, vol.22, no.2, pp.799-805, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.18514/mmn.2021.3661
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.799-805
  • Keywords: essential submodules, g-small submodules, generalized radical, g-supplemented mod-ules
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Let M be an R-module. If every essential submodule of M has a g-radical supplement in M, then M is called an essential g-radical supplemented (or briefly eg-radical supplemented) module. In this work, some properties of these modules are investigated. It is proved that every factor module and every homomorphic image of an eg-radical supplemented module are eg-radical supplemented. Let M be an eg-radical supplemented module. Then every finitely M-generated R-module is eg-radical supplemented.