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A commutativity result for rings

Published online by Cambridge University Press:  17 April 2009

A. A. Klein  and
I. Nada
A. A. Klein
Affiliation:
School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel.
I. Nada
Affiliation:
School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel.
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Abstract

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It is proved that a ring satisfying the variable indentity [[xn, y], y] = 0, n = n (x,y) ≥ 1, has nil commutator ideal.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 3 , June 1986 , pp. 359 - 362
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Herstein, I.N., ‘Two remarks on the commutativity of rings’, Canad. J. Math., 7 (1955), 411–412.Google Scholar
[2]Herstein, I.N., ‘On rings with a particular variable identity’, J. Algebra, 62 (1980), 346–357.CrossRefGoogle Scholar
[3]Klein, A.A., Nada, I. and Bell, H.E., ‘Some commutativity results for rings’, Bull. Austral. Math. Soc., 22 (1980), 285–289.CrossRefGoogle Scholar