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Turkish Journal of Mathematics

DOI

-

Abstract

This article introduces the concept of a \tau-supplemented module as follows: Given a hereditary torsion theory in Mod R with associated torsion functor \tau, we say that a module M is \tau-supplemented when for every submodule N of M there exists a direct summand K of M such that K\leq N and N/K is \tau-torsion module. We present here some fundamental properties of this class of modules and study the decompositions of \tau-supplemented modules under certain conditions on modules. The question of which direct sum of \tau-supplemented R-modules are \tau-supplemented is treated here.

First Page

177

Last Page

184

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