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τ -supplemented modules and τ -weakly supplemented modules

Muhammet Tamer Koşan (2007)

Archivum Mathematicum

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 τ ( V ) and M is τ -weakly supplemented if every submodule...

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