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Commutativity results for rings
Published online by Cambridge University Press: 17 April 2009
Abstract
Let R be an associative ring. We prove that if for each finite subset F of R there exists a positive integer n = n(F) such that (xy)n − yn xn is in the centre of R for every x, y in F, then the commutator ideal of R is nil. We also prove that if n is a fixed positive integer and R is an n(n + 1)-torsion-free ring with identity such that (xy)n − ynxn = (yx)n xnyn is in the centre of R for all x, y in R, then R is commutative.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 38 , Issue 2 , October 1988 , pp. 191 - 195
- Copyright
- Copyright © Australian Mathematical Society 1988
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