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International Journal of Mathematics and Mathematical Sciences
Volume 17, Issue 1, Pages 65-72
http://dx.doi.org/10.1155/S0161171294000104

A result of commutativity of rings

Department of Mathematics, M.D. University, P.G. Regional Centre, Rewari, (Haryana), India

Received 11 December 1990; Revised 9 September 1991

Copyright © 1994 Hindawi Publishing Corporation. 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 prove the following:

THEOREM. Let n>1 and m be fixed relatively prime positive integers and k is any non-negative integer. If R is a ring with unity 1 satisfying xk[xn,y]=[x,ym] for all x,yR then R is commutative.