Pure Mathematics for Theoretical Computer Science PMTCS 2995-3162 10.54216/PMTCS https://www.americaspg.com/journals/show/2135 2023 2023 Faculty of Science, Mutah University, Jordan Rashel Abu Hakmeh 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. 2023 2023 34 38 10.54216/PMTCS.020104 https://www.americaspg.com/articleinfo/40/show/2135