A variation of supplemented modules

BİLHAN G., Guroglu A. T.

TURKISH JOURNAL OF MATHEMATICS, vol.37, no.3, pp.418-426, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 3
  • Publication Date: 2013
  • Doi Number: 10.3906/mat-1108-20
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.418-426
  • Keywords: Modules, omega-supplemented, Dedekind domain
  • Dokuz Eylül University Affiliated: Yes

Abstract

Over a general ring, an R-module is omega-supplemented if and only if amply omega-supplemented. It is proved that over a local Dedekind domain, all modules are omega-supplemented and over a non-local Dedekind domain, an R-module M is omega-supplemented if and only if Soc(M) << M or M = S-0 circle plus (circle plus(i is an element of I) K), where S-0 is a torsion, semisimple submodule of M and K is the field of quotients of R.