• A CHARACTERIZATION OF DUO-RINGS IN WHICH EVERY DEDEKING FINITE MODULE IS FINITELY GENERATED

*Sidy Demba Touré, Mamadou Sangharé, Sidy Mohamed Ould Mohamed

Abstract


Let R be an associative ring with 1  0 and M an unitary R-module. M is said to be Dedekind finite if M is not isomorphic to any proper direct summand of itself. The ring R is called FGDF ring if every Dedekind finite module is finitely generated. In this note we will prove that artinian principal ideal duo-rings characterize FGDF-duo-rings.

Keywords


Dedeking finite modules, hopfian modules, Artinian principal ideal rings, Duo-rings.

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