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Variations on a Theme: Rings Satisfying x3 = x Are Commutative

Stephen M. Buckley and Desmond MacHale
The American Mathematical Monthly
Vol. 120, No. 5 (May 2013), pp. 430-440
DOI: 10.4169/amer.math.monthly.120.05.430
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.120.05.430
Page Count: 11
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Variations on a Theme: Rings Satisfying x3 = x Are Commutative
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Abstract

Abstract A ring satisfying x3 = x is necessarily commutative. We consider a variety of weaker forms of this condition and show that many, but not all of them, imply commutativity. We also present a variety of elementary proofs of the fact that x3 = x implies commutativity.

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