Modules having a weak rad-supplement in every cofinite extension

Onal Kir E., Çalışıcı H.

JOURNAL OF POLYTECHNIC-POLITEKNIK DERGISI, 2022 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.2339/politeknik.991518
  • Journal Name: JOURNAL OF POLYTECHNIC-POLITEKNIK DERGISI
  • Journal Indexes: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
  • Keywords: Weak Rad-supplement, semilocal ring, cofinite extension
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this study, we introduce the modules with the properties (CWRE) and (CWREE) as a generalization of the modules with the properties (CWE) and (CWEE). Let R be a ring and M be a left R-module. If M has the property (CWRE), then every direct summand of M has the property (CWRE). A ring R is semilocal if and only if every left R-module has the property (CWRE). We also study the modules that have the properties (WRE*) and (WREE*). A module has the property (WREE*) if and only if every submodule of it has the property (WRE*).