Duo modules


ÖZCAN A. Ç. , HARMANCI A., Smith P. F.

GLASGOW MATHEMATICAL JOURNAL, vol.48, pp.533-545, 2006 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48
  • Publication Date: 2006
  • Doi Number: 10.1017/s0017089506003260
  • Journal Name: GLASGOW MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.533-545

Abstract

Let R be a ring. An R-module M is called a (weak) duo module provided every (direct summand) submodule of M is fully invariant. It is proved that if R is a commutative domain with field of fractions K then a torsion-free uniform R-module is a duo module if and only if every element k in K such that kM is contained in M belongs to R. Moreover every non-zero finitely generated torsion-free duo R-module is uniform. In addition, if R is a Dedekind domain then a torsion R-module is a duo module if and only if it is a weak duo module and this occurs precisely when the P-primary component of M is uniform for every maximal ideal P of R.