We show that ifRis an exchange ring, then the following are equivalent: (1)Rsatisfies related comparability. (2) Givena,b,d∈RwithaR+bR=dR, there exists a related unitw∈Rsuch thata+bt=dw. (3) Givena,b∈RwithaR=bR, there exists a related unitw∈Rsuch thata=bw. Moreover, we investigate the dual problems for rings which are quasi-injective as right modules.
Elements in exchange rings with related comparability