International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 9, Pages 639-644
Elements in exchange rings with related comparability
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 is an exchange ring, then the following are
equivalent: (1) satisfies related comparability. (2) Given
with , there exists a related unit such that . (3) Given with , there exists a related unit such that . Moreover, we investigate the dual problems for rings which are quasi-injective as right modules.