Modules with Unique Closure Relative to a Torsion Theory. III

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Dogruoz S., Harmanci A., Smith P. F.

UKRAINIAN MATHEMATICAL JOURNAL, vol.66, no.7, pp.1028-1036, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 66 Issue: 7
  • Publication Date: 2014
  • Doi Number: 10.1007/s11253-014-0992-x
  • Journal Name: UKRAINIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1028-1036
  • Hacettepe University Affiliated: Yes

Abstract

We continue the study of modules over a general ring R whose submodules have a unique closure relative to a hereditary torsion theory on Mod-R. It is proved that, for a given ring R and a hereditary torsion theory tau on Mod-R, every submodule of every right R-module has a unique closure with respect to tau if and only if tau is generated by projective simple right R-modules. In particular, a ring R is a right Kasch ring if and only if every submodule of every right R-module has a unique closure with respect to the Lambek torsion theory.