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On Rings With Engel Cycles

Published online by Cambridge University Press:  20 November 2018

H. E. Bell  and
A. A. Klein
H. E. Bell
Affiliation:
Mathematics Department, Brock University, St. Catharines, Ontario L2S 3A1
A. A. Klein
Affiliation:
Raymond and Beverly Sackler Faculty of Exact Sciences, School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, 69978 Tel-Aviv, Israel
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Abstract

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A ring R is called an EC-ring if for each x, y ∊ R, there exist distinct positive integers m, n such that the extended commutators [x, y]m and [x, y]n are equal. We show that in certain EC-rings, the commutator ideal is periodic; we establish commutativity of arbitrary EC-domains; we prove that a ring R is commutative if for each x, y ∊ R, there exists n > 1 for which [x, y] = [x, y]n.

Keywords

16A7016A1516A38
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 3 , 01 September 1991 , pp. 295 - 300
Copyright
Copyright © Canadian Mathematical Society 1991

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