International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 2, Pages 409-411
doi:10.1155/S0161171297000549
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 Vishnu Gupta. 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 that if R is a ring with 1 as an identity element in which
xm−xn∈Z(R) for all x∈R 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)n∈Z(R) for all x∈R and fixed positive integer n and non-negative integer k, then
R is commutative.