MODULES THAT HAVE A WEAK RAD-SUPPLEMENT IN EVERY EXTENSION

Kir E. O., Çalışıcı H.

JOURNAL OF SCIENCE AND ARTS, no.3, pp.611-616, 2018 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2018
  • Journal Name: JOURNAL OF SCIENCE AND ARTS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.611-616
  • Keywords: weak Rad-supplement, extension, semilocal ring, Von Neumann regular ring, RINGS
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

As a proper generalization of the modules with the properties (E) and (EE) that were introduced by Zoschinger in terms of supplements, we say that a module M has the property (WRE) (respectively, (WREE)) if M has a weak Rad-supplement (respectively, ample weak Rad-supplements) in every extension. In this paper, we prove that if every submodule of a module M has the property (WRE), then M has the property (WREE). We show that a ring R is semilocal if and only if every left R-module has the property (WRE). Also we prove that over a commutative Von Neumann regular ring a module M has the property (WRE) if and only if M is injective.