ESSENTIAL RADICAL SUPPLEMENTED MODULES

Nebiyev C.

MISKOLC MATHEMATICAL NOTES, vol.22, no.1, pp.427-434, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.18514/mmn.2021.3215
  • Journal Name: MISKOLC MATHEMATICAL NOTES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.427-434
  • Keywords: small submodules, essential submodules, radical, generalized (radical) supplemented modules
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this work, (amply) essential radical supplemented modules are defined and some properties of these modules are investigated. Let M be an R-module and M = M-1 + M-2 + ... + M-n. If M-i is essential radical supplemented for every i = 1, 2, ..., n, then M is also essential radical supplemented. It is proved that every factor module and every homomorphic image of an essential radical supplemented module are essential radical supplemented. Let M be an essential radical supplemented R-module. Then every finitely M-generated R-module is essential radical supplemented.