Abstract

In [19], Thuyet and Wisbauer considered the extending property for the class of (essentially) finitely generated submodules. A module M is called ef-extending if every closed submodule which contains essentially a finitely generated submodule is a direct summand of M. A ring R is called right ef-extending if RR is an ef-extending module. We show that a ring R is QF if and only if R is a left Noetherian, right GP-injective and right efextending ring. Moreover, we prove that R is right PF if and only if R is a right cogenerator, right ef-extending and I-finite.