1. Modules Supplemented Relative to A Torsion Theory.
- Author
-
Kosan, Tamer and Harmanci, Abdullah
- Subjects
- *
MODULES (Algebra) , *TORSION theory (Algebra) , *FINITE groups , *RING theory , *ALGEBRA - Abstract
This article introduces the concept of a τ-supplemented module as follows: Given a hereditary torsion theory in Mod R with associated torsion functor τ, we say that a module M is τ-supplemented when for every submodule N of M there exists a direct summand K of M such that K ≤ N and N/K is τ-torsion module. We present here some fundamental properties of this class of modules and study the decompositions of τ-supplemented modules under certain conditions on modules. The question of which direct sum of τ-supplemented R-modules are τ-supplemented is treated here. [ABSTRACT FROM AUTHOR]
- Published
- 2004