Two elementary commutativity theorems for generalized boolean rings

Vishnu Gupta

International Journal of Mathematics and Mathematical Sciences, 1997, vol. 20, 1-3

Abstract:

In this paper we prove that if R is a ring with 1 as an identity element in which x m − x n ∈ 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 ( x 2 k ) n + 1 − ( x 2 k ) n ∈ Z ( R ) for all x ∈ R and fixed positive integer n and non-negative integer k , then R is commutative.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:926523

DOI: 10.1155/S0161171297000549

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