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On the commutativity of semi-prime rings

Published online by Cambridge University Press:  09 April 2009

Abdullah H. Al-Moajil
Abdullah H. Al-Moajil
Affiliation:
Gulf Organization for Industrial Consulting, P.O. Box 5114, Doha, Quatar
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Abstract

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It is shown that if R is a 2-torsion-free semi-prime ring such that [xy, [xy, yx]] = 0 for all x, y ∈ R, then R is commutative.

Keywords

nilpotentnilpotent idealsemi-prime
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 1 , January 1982 , pp. 48 - 51
Copyright
Copyright © Australian Mathematical Society 1982

References

[1] Awtar, R., ‘A remark on the commutativity of certain rings’, Proc. Amer. Math. Soc. 41 1973, 370–372.CrossRefGoogle Scholar
[2] Gupta, R., ‘Nilpotent matrices with invertible transpose’, Proc. Amer. Math. Soc. 24 1970, 572–575.CrossRefGoogle Scholar
[3] Herstein, I., Non-commutative rings, (Carus Monograph 16, Mathematical Association of America, Washington D.C., 1968).Google Scholar
[4] Herstein, I., Topics in ring theory, (University of Chicago Press, 1969).Google Scholar
[5] Herstein, I., ‘A commutativity theorem’, J Algebra 38 1976, 112–118.Google Scholar
[6] Jacobson, N., Structure of rings, (Amer. Math. Soc. Colloquium Publications 37, Amer. Math. Soc., Providence, R.I., 1964).Google Scholar