International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 9, Pages 639-644
doi:10.1155/S0161171200002234

Elements in exchange rings with related comparability

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.