Abstract

We show that if R is an exchange ring, then the following are equivalent: (1) R satisfies related comparability. (2) Given a,b,d∈R with aR+bR=dR, there exists a related unit w∈R such that a+bt=dw. (3) Given a,b∈R with aR=bR, there exists a related unit w∈R such that a=bw. Moreover, we investigate the dual problems for rings which are quasi-injective as right modules.