Dedekind modules

Alkan M., Sarac B., Tiras Y.

COMMUNICATIONS IN ALGEBRA, vol.33, no.5, pp.1617-1626, 2005 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 5
  • Publication Date: 2005
  • Doi Number: 10.1081/agb-200061007
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1617-1626
  • Keywords: Dedekind modules and Dedekind domains, integrally closed, invertible submodules, MULTIPLICATION MODULES, DENSE SUBMODULES
  • Hacettepe University Affiliated: Yes

Abstract

In this paper, the authors introduce the concept of integrally closed modules and characterize Dedekind modules and Dedekind domains. They also show that a given domain R is integrally closed if and only if a finitely generated torsion-free projective R-module is integrally closed. In addition, it is proved that any invertible submodule of a finitely generated projective module over a domain is finitely generated and projective. Also they give the equivalent conditions for Dedekind modules and Dedekind domains.