2019
Том 71
№ 11

All Issues

Doğruöz S.

Articles: 1
Article (English)

Modules with Unique Closure Relative to a Torsion Theory. III

Doğruöz S., Harmanci A., Smith P. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 7. - pp. 922–929

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.