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

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.