International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 2, Pages 267-270
Commutativity of one sided -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.
The main theorem proved in the present paper states as follows Let , , and be
fixed non-negative integers such that and are not simultaneously equal to and be a left
(resp right) -unital ring satisfying (resp ) Then is
commutative. Further commutativity of left -unital rings satisfying the condition where and and 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 and for their values.
These results generalize a number of commutativity theorems established recently.