TY - JOUR
AU - S. Doğruöz
AU - A. Harmanci
AU - P. F. Smith
PY - 2014/07/25
Y2 - 2023/03/29
TI - Modules with Unique Closure Relative to a Torsion Theory. III
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 66
IS - 7
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2188
AB - 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.
ER -