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

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.