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On a commutativity theorem for semi-simple rings

Published online by Cambridge University Press:  17 April 2009

Murtaza A. Quadri  and
Mohd. Ashraf
Murtaza A. Quadri
Affiliation:
Department of Mathematics, Aligarh Muslim University, Aligarh 202001, India.
Mohd. Ashraf
Affiliation:
Department of Mathematics, Aligarh Muslim University, Aligarh 202001, India.
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Abstract

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In this note a theorem proved by Abu-Khuzam and Yaqub has been improved as follows: let R be a semi-simple ring such that for all x, y in R there exists a positive integer n = n(x, y) for which either (xy)n + (yx)n or (xy)n – (yx)n is central. Then R is commutative.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 3 , June 1985 , pp. 365 - 368
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Hazar, Abu-Khuzam and Adil, Yaqub, “A commutativity theorem for division rings”, Bull. Austral. Math. Soc. 21 (1980), 43–46.Google Scholar
[2]Herstein, I.N., “A commutativity theorem”, J. Algebra 38 (1976), 112–118.CrossRefGoogle Scholar
[3]Posner, E.C., “Derivations in prime rings”, Proc. Amer. Math. Soc. 8 (1951), 1093–1100.CrossRefGoogle Scholar