A Discussion of FGF Conjecture in Some Quasi-Frobenus Rings

Rashel Abu Hakmeh

Faculty of Science, Mutah University, Jordan

Abstract

A ring R is called right FGF ring, if every finitely generated right R-module embeds in a free right R-module. It is well known that a quasi-Frobenus ring R is right FGF ring, but the converse is still an open question. In this note we give some equivalent additional conditions that convert the right FGF ring to the QF ring. Other known results that characterize the class of quasi-Frobenius rings are fond. In the process, some new results that characterize the class of IF-rings are provided.

Keywords: QF- ring; FGF-ring; IF-ring; FP-injective module; Flat module.