International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 2, Pages 267-270
doi:10.1155/S0161171297000367
Commutativity of one sided s-unital rings through a Streb's result
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Received 4 October 1994; Revised 19 September 1995
Copyright © 1997 Murtaza A. Quadri et al. 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 main theorem proved in the present paper states as follows “Let m, k, n and s be
fixed non-negative integers such that k and n are not simultaneously equal to 1 and R be a left
(resp right) s-unital ring satisfying [(xmyk)n−xsy,x]=0 (resp [(xmyk)n−yxs,x]=0) Then R is
commutative.” Further commutativity of left s-unital rings satisfying the condition xt[xm,y]−yr[x,f(y)]xs=0 where f(t)∈t2Z[t] and m>0,t,r and s are fixed non-negative integers, has been
investigated Finally, we extend these results to the case when integral exponents in the underlying
conditions are no longer fixed, rather they depend on the pair of ring elements x and y for their values.
These results generalize a number of commutativity theorems established recently.