Geodesic
On the Power Map and Ring Commutativity
Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 399-404

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Bell, Howard E. On the Power Map and Ring Commutativity. Canadian mathematical bulletin, Tome 21 (1978) no. 4, pp. 399-404. doi: 10.4153/CMB-1978-070-x
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