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International Journal of Mathematics and Mathematical Sciences
Volume 20, Issue 2, Pages 409-411

Two elementary commutativity theorems for generalized boolean rings

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

Received 9 September 1991; Revised 17 April 1992

Copyright © 1997 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.


In this paper we prove that if R is a ring with 1 as an identity element in which xmxnZ(R) for all xR and fixed relatively prime positive integers m and n, one of which is even, then R is commutative. Also we prove that if R is a 2-torsion free ring with 1 in which (x2k)n+1(x2k)nZ(R) for all xR and fixed positive integer n and non-negative integer k, then R is commutative.