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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 closed submodule, $UC$-module, torsion theory
MSC Classifications: 16S90 show english descriptions Torsion theories; radicals on module categories [See also 13D30, 18E40] {For radicals of rings, see 16Nxx} 16S90 - Torsion theories; radicals on module categories [See also 13D30, 18E40] {For radicals of rings, see 16Nxx}
 

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