International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 4, Pages 769-774

A commutativity theorem for left s-unital rings

Hamza A. S. Abujabal

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 R be a left s-unital ring. If there exist nonnegative integers m>1, k0, and n0 such that for any x, y in R, [xkyxnym,x]=0, then R is commutative.