Some properties of AF G and CT F rings

Abstract

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