Dergiler / Turkish Journal of Mathematics / 2004 / Cilt: 28 - Sayı: 2
Modules Supplemented Relative to A Torsion Theory
- Sayfa
- 177–184
- DOI
- —
Özet
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.
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.