Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-23T03:23:31.522Z Has data issue: false hasContentIssue false

On the commutativity of torsion free rings

Published online by Cambridge University Press:  17 April 2009

Evagelos Psomopoulos
Affiliation:
Department of Mathematics, University of Thessaloniki, Thessaloniki, Greece.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If R is (n(n−1)/2)-torsion free ring with 1 and satisfies the identity (xy)n = xnyn, then R is commutative provided that n = 4k.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Abu-Khuzam, H., “A commutativity theorem for rings”. Math. Japon. 25 (1980), 593595.Google Scholar
[2]Bell, H.E., “On the power map and ring commutativity”, Canad. Math. Bull. 21 (1978), 399404.CrossRefGoogle Scholar
[3]Herstein, I.N., “Power maps in rings”, Michigan Math. J. 8 (1961), 2932.CrossRefGoogle Scholar
[4]Kobayashi, Y., “Some polynomial identities and commutativity of rings, I”, Proc. 14th Sympos. Ring Theory, 1981, 18 (Matsumoto, Japan, 1981).Google Scholar