Modules with Unique Closure Relative to a Torsion Theory. III

  • S. Doğruöz
  • A. Harmanci
  • P. F. Smith

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 τ on Mod-R, every submodule of every right R-module has a unique closure with respect to τ if and only if τ 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.
Published
25.07.2014
How to Cite
DoğruözS., HarmanciA., and SmithP. F. “Modules With Unique Closure Relative to a Torsion Theory. III”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 7, July 2014, pp. 922–929, http://umj.imath.kiev.ua/index.php/umj/article/view/2188.
Section
Research articles