Modules with Unique Closure Relative to a Torsion Theory. III

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 res...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2014-12, Vol.66 (7), p.1028-1036
Main Authors: Doğruöz, S., Harmanci, A., Smith, P. F.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Statistics
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Summary: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.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-014-0992-x