Modules Supplemented Relative to A Torsion Theory
Authors : Tamer Koşan, Abdullah Harmanci
Pages : 177-184
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Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :This article introduces the concept of a t-supplemented module as follows: Given a hereditary torsion theory in Mod R with associated torsion functor t, we say that a module M is t-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 t-torsion module. We present here some fundamental properties of this class of modules and study the decompositions of t-supplemented modules under certain conditions on modules. The question of which direct sum of t-supplemented R-modules are t-supplemented is treated here.Keywords : Torsion Theory, Supplemented Module