Duo modules


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

GLASGOW MATHEMATICAL JOURNAL, cilt.48, ss.533-545, 2006 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 48
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1017/s0017089506003260
  • Dergi Adı: GLASGOW MATHEMATICAL JOURNAL
  • Sayfa Sayıları: ss.533-545

Özet

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.