International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 4, Pages 769-774
doi:10.1155/S0161171290001065
A commutativity theorem for left s-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.
Abstract
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, k≥0, and n≥0 such that for any x, y in R, [xky−xnym,x]=0, then R is commutative.