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A commutativity theorem for semiprime rings
Published online by Cambridge University Press: 17 April 2009
Abstract
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Let R be a semiprime ring in which for each x in R there exists a positive integer n = n(x) < 1 such that (xy)n = xnyn for all y in R. Then R is commutative.
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- Copyright © Australian Mathematical Society 1983
References
[1]Abu-Khuzam, Hazar, “A commutativity theorem for rings”, Math. Japon. 25 (1980), 593–595.Google Scholar
[2]Bell, Howard E., “On the power map and ring commutativity”, Canad. Math. Bull. 21 (1978), 399–404.CrossRefGoogle Scholar
[5]Herstein, I.N., Rings with involution (University of Chicago Press, Chicago, London, 1976).Google Scholar
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