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