Geodesic
On Rings With Engel Cycles
Canadian mathematical bulletin, Tome 34 (1991) no. 3, pp. 295-300

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DOI

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 .
DOI : 10.4153/CMB-1991-048-x
Mots-clés : 16A70, 16A15, 16A38 
Bell, H. E.; Klein, A. A. On Rings With Engel Cycles. Canadian mathematical bulletin, Tome 34 (1991) no. 3, pp. 295-300. doi: 10.4153/CMB-1991-048-x
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     title = {On {Rings} {With} {Engel} {Cycles}},
     journal = {Canadian mathematical bulletin},
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     year = {1991},
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     number = {3},
     doi = {10.4153/CMB-1991-048-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-048-x/}
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