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A theorem on commutativity of semi-prime 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 202 001, (India).
Mohd. Ashraf
Affiliation:
Department of Mathematics, Aligarh Muslim University, Aligarh 202 001, (India).
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Abstract

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The following Theorem is proved: Let R be a semi-prime ring in which either (xy)n − xnyn or (xy)n − ynxn is central, for all x,y in R where n > 1 is a fixed integer. Then R is commutative.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 3 , December 1986 , pp. 411 - 413
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Abu-Khuzam, Hazar, “Acommutativity theorem for rings”, Math. Japan. 25 (1980), 593–595.Google Scholar
[2]Abu-Khuzam, Hazar, “A commutativity theorem for semi-prime rings’, Bull. Austral. Math. Soc. 27 (1983), 221–224.CrossRefGoogle Scholar
[3]Awtar, R., “On the commutativity of non-associative rings”, Publ. Math. Debrecen, 22 (1975), 177–188.CrossRefGoogle Scholar
[4]Bell, H. E., “On some commutativity theorem of Herstein”, Arch. Math. (Basel) 24 (1973), 34–38.CrossRefGoogle Scholar
[5]Bell, H. E., “On the power map and ring commutativity’, Canad. Math. Bull. 21 (1978), 399–404.CrossRefGoogle Scholar
[6]Herstein, I. N., “Power Maps in rings”, Michigan Math. J. 8 (1961), 29–32.CrossRefGoogle Scholar
[7]Herstein, I. N., Topics in Ring theory, (University of Chicago Press, Chicago, London, 1969).Google Scholar