Global Journal of Pure and Applied Mathematics

A unital left R-module _RM is said to have property (S) if every surjective endomorphism of _RM is an automorphism, the ring R is called left (right) FGS-ring if every left (right) R-module with property (S) is finitely generated, R is called FGS-ring if it is both a left and right FGS-ring. A ring R is called duo – ring if every left (right) ideal of R is a two sided ideal. In this note we show that a duoring is a FGS-ring if and only if it is an Artinian principal ideal ring.