International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 4, Pages 769-774
A commutativity theorem for left -unital rings
Department of Mathematics, Faculty of Science, King Abdul-Aziz University, P.O. BOX 9028, Jeddah 21413, Saudi Arabia
Received 2 June 1989; Revised 25 July 1989
Copyright © 1990 Hamza A. S. Abujabal. 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.
In this paper we generalize some well-known commutativity theorems for associative rings as follows: Let be a left -unital ring. If there exist nonnegative integers , , and such that for any , in , , then is commutative.