On invertible and dense submodules

ALKAN M., Tıraş Y.

COMMUNICATIONS IN ALGEBRA, vol.32, no.10, pp.3911-3919, 2004 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 10
  • Publication Date: 2004
  • Doi Number: 10.1081/agb-200027783
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3911-3919
  • Keywords: invertible submodules, dense submodules, projective submodules, locally free submodules, Dedekind domain, MULTIPLICATION MODULES
  • Akdeniz University Affiliated: No

Abstract

In this paper, the authors give a partial characterization of invertible, dense and projective submodules. In the final section, they give the equivalent conditions to be invertible, dense and projective submodules for a given an R-module M. They also provide conditions under which a given ring R is a Dedekind domain if and only if every non zero submodule of an R-module is locally free.