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# Modules with Unique Closure Relative to a Torsion Theory

Published:2009-12-04
Printed: Jun 2010
• S. Doğruöz
• A. Harmanci
• P. F. Smith
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## Abstract

We consider when a single submodule and also when every submodule of a module M over a general ring R has a unique closure with respect to a hereditary torsion theory on $\operatorname{Mod}$-R.
 Keywords: closed submodule, $UC$-module, torsion theory
 MSC Classifications: 16S90 - Torsion theories; radicals on module categories [See also 13D30, 18E40] {For radicals of rings, see 16Nxx}

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