2017
Том 69
№ 9

All Issues

Modules with Unique Closure Relative to a Torsion Theory. III

Doğruöz S., Harmanci A., Smith P. F.

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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.

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 7, pp 1028-1036.

Citation Example: Doğruöz S., Harmanci A., Smith P. F. Modules with Unique Closure Relative to a Torsion Theory. III // Ukr. Mat. Zh. - 2014. - 66, № 7. - pp. 922–929.

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