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.
Torsion Theory, Supplemented Module
KOŞAN, M. TAMER and HARMANCI, ABDULLAH (2004) "Modules Supplemented Relative to A Torsion Theory," Turkish Journal of Mathematics: Vol. 28: No. 2, Article 8. Available at: https://journals.tubitak.gov.tr/math/vol28/iss2/8