aspg-40-2135-1792533366 20261020215606 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Pure Mathematics for Theoretical Computer Science PMTCS 2995-3162 2023 2 1 Rashel Abu Hakmeh Faculty of Science, Mutah University, Jordan 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 34 38 2135 https://creativecommons.org/licenses/by/4.0/ 10.54216/PMTCS.020104 https://americaspg.com/journal/40/article/2135 https://americaspg.com/storage/21696385621.pdf