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Two elementary commutativity theorems for generalized boolean rings

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  • Vishnu Gupta

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.

Suggested Citation

  • Vishnu Gupta, 1997. "Two elementary commutativity theorems for generalized boolean rings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 20, pages 1-3, January.
    • Handle: RePEc:hin:jijmms:926523
    DOI: 10.1155/S0161171297000549
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