Generalizations of rad-supplemented modules

Kaynar E., Türkmen E., Aydin Y.

Publications de l'Institut Mathematique, vol.104, no.118, pp.139-148, 2018 (Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 104 Issue: 118
  • Publication Date: 2018
  • Doi Number: 10.2298/pim1818139k
  • Journal Name: Publications de l'Institut Mathematique
  • Journal Indexes: Scopus
  • Page Numbers: pp.139-148
  • Keywords: preradical, Jacobson radical, Rad-supplement, tau-supplement, Communicated by Zoran Petrovic
  • Istanbul Gelisim University Affiliated: No

Abstract

Let R be an associative ring with identity. We introduce the notion of semi-τ-supplemented modules, which is adapted from srs-modules, for a preradical τ on R-Mod. We provide basic properties of these modules. In particular, we study the objects of R-Mod for τ = Rad. We show that the class of semi-τ-supplemented modules is closed under finite sums and factor modules. We prove that, for an idempotent preradical τ on R-Mod, a module M is semi-τ-supplemented if and only if it is τ-supplemented. For τ = Rad, over a local ring every left module is semi-Rad-supplemented. We also prove that a commutative semilocal ring whose semi-Rad-supplemented modules are a direct sum of w-local left modules is an artinian principal ideal ring.