Duo modules

Ozcan, A.C., Harmanci, A. and Smith, P.F. (2006) Duo modules. Glasgow Mathematical Journal, 48(3), pp. 533-545. (doi: 10.1017/S0017089506003260)

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Smith, Professor Patrick
• Authors: Ozcan, A.C., Harmanci, A., and Smith, P.F.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Glasgow Mathematical Journal
• Publisher: Cambridge University Press
• ISSN: 0017-0895
• ISSN (Online): 1469-509X
• Published Online: 06 December 2006
• Copyright Holders: Copyright © 2006 Glasgow Mathematical Journal Trust
• First Published: First published in Glasgow Mathematical Journal 48(3):533-545
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher