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On rings with nil commutator ideal

Published online by Cambridge University Press:  17 April 2009

Hazar Abu-Khuzam
Hazar Abu-Khuzam
Affiliation:
Department of Mathematical Sciences, University of Petroleum and Minerals, Drahran, Saudi Arabia.
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Abstract

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Let R be a ring in which for each x, y in R there exists a positive integer n = n(x, y) such that (xy)n − (yx)n is in the center of R. Then R has a nil commutator ideal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 2 , April 1981 , pp. 307 - 311
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Abu-Khuzam, Hazar and Yaqub, Adil, “A comnutativity theorem for division rings”, Bull. Austral. Math. Soc. 21 (1980), 43–46.CrossRefGoogle Scholar
[2]Belluce, L.P., Herstein, I.N. and Jain, S.K., “Generalized commutative rings”, Nagoya Math. J. 27 (1966), 1–5.CrossRefGoogle Scholar
[3]Herstein, I.N., “A commutativity theorem”, J. Algebra 38 (1976), 112–118.CrossRefGoogle Scholar
[4]Herstein, I.N., Rings with involution (University of Chicago Press, Chicago, Illinois; London; 1976).Google Scholar