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A commutativity theorem for semi-primitive rings

Published online by Cambridge University Press:  17 April 2009

Hisao Tominaga
Hisao Tominaga
Affiliation:
Department of Mathematics, Okayama University, Okayama 700, Japan.
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Abstract

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In this brief note, we prove the following: Let R be a semi-primitive ring. Suppose that for each pair x, y ε R there exist positive integers m = m (x,y) and n = n (x,y) such that either [xm,(xy) n − (yx) n] = 0 or [xm,(xy) n + (yx) n] = 0. Then R is commutative.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 2 , October 1986 , pp. 293 - 295
Copyright
Copyright © Australian Mathematical Society 1986

References

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