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
Hamza A.S. Abujabal
Department of Mathematics, Faculty of Science, King Abdul-Aziz University, P.O. BOX 9028, Jeddah 21413, Saudi Arabia
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.