R is said to be a right AFG ring if the right annihilator of everynonempty subset of R is a finitely generated right ideal. R is calleda right CTF ring if every cyclic torsionless right R-module embeds in afree module. In this paper, we first give new characterizations of AFGrings and study some closure properties of AFG rings. Then we explorethe intimate relationships between AFG rings and CTF rings.