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On the Power Map and Ring Commutativity

Published online by Cambridge University Press:  20 November 2018

Howard E. Bell
Howard E. Bell*
Affiliation:
Department of Mathematics, Brock University, St. Catharines, Ontario, Canada, L2S 3A1
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Let R denote an associative ring with 1, let n be a positive integer, and let k = 1, 2, or 3. The ring R will be called an (n, k)-ring if it satisfies the identities

for all integers m with n ≤ m ≤ n + k - 1. It was shown years ago by Herstein (See [2], [9], and [10]) that for n >1, any (n, l)-ring must have nil commutator ideal C(R). Later Luh [12] proved that primary (rc, 3)-rings must in fact be commutative, and Ligh and Richoux [11] recently showed that all (n, 3)-rings are commutative.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 4 , 01 December 1978 , pp. 399 - 404
Copyright
Copyright © Canadian Mathematical Society 1978

References

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