Amply (weakly) Goldie-Rad-supplemented modules

TAKIL MUTLU F.

Algebra & Discrete Mathematics, vol.22, no.1, pp.94-101, 2016 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 1
  • Publication Date: 2016
  • Journal Name: Algebra & Discrete Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.94-101
  • Keywords: Supplement submodule, Goldie-Rad-Supplement submodule, amply Goldie-Rad-Supplemented module
  • Anadolu University Affiliated: No

Abstract

Let R be a ring and M be a right R-module. We say a submodule S of M is a (weak) Goldie-Rad-supplement of a submodule N in M, if M = N + S, (N boolean AND S <= Rad(M)) N boolean AND S <= Rad(S) and N beta**S, andM is called am ply (weakly)Goldie-Rad-supplemented if every submodule of M has ample (weak) Goldie-Rad-supplements in M. In this paper we study various properties of such modules. We show that every distributive projective weakly Goldie-Rad-Supplemented module is amply weakly Goldie-Rad-Supplemented. We also show that if M is amply (weakly) Goldie-Rad- supplemented and satisfies DCC on (weak) Goldie-Rad-supplement submodules and on small submodules, then M is Artinian.