1. τ-SUPPLEMENTED MODULES AND τ-WEAKLY SUPPLEMENTED MODULES.
- Author
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Koşsan, Muhammet Tamer
- Subjects
- *
TORSION theory (Algebra) , *MODULES (Algebra) , *ASSOCIATIVE rings , *RING theory , *ALGEBRA - Abstract
Given a hereditary torsion theory τ = (T,F) in Mod-R, a module M is called τ-supplemented if every submodule A of M contains a direct summand C of M with A/C τ-torsion. A submodule V of M is called τ - supplement of U in M if U + V = M and U ∩ V ≤(V) and M is τ - weakly supplemented if every submodule of M has a τ-supplement in M. Let M be a τ-weakly supplemented module. Then M has a decomposition M = M1 ⊕ M2 where M1 is a semisimple module and M2 is a module with τ(M2) ≤e M2. Also, it is shown that; any finite sum of τ-weakly supplemented modules is a τ-weakly supplemented module. [ABSTRACT FROM AUTHOR]
- Published
- 2007