International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 9, Pages 639-644

Elements in exchange rings with related comparability

Huanyin Chen

Department of Mathematics, Hunan Normal University, Changsha 410006, China

Received 23 December 1998

Copyright © 2000 Huanyin Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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