International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 4, Pages 813-818
doi:10.1155/S0161171292001078
On commutativity of one-sided s-unital rings
Department of Mathematics, Faculty of Science, King Abdul Aziz University, P. O. Box 31464, Jeddah 21497, Saudi Arabia
Received 11 October 1990; Revised 18 December 1990
Copyright © 1992 H. A. S. Abujabal and M. A. Khan. 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
The following theorem is proved: Let r=r(y)>1, s, and t be non-negative integers. If R is a left s-unital ring satisfies the polynomial identity [xy−xsyrxt,x]=0 for every x,y∈R, then R is commutative. The commutativity of a right s-unital ring satisfying the polynomial identity [xy−yrxt,x]=0 for all x,y∈R, is also proved.