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

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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. 
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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     title = {On the {Power} {Map} and {Ring} {Commutativity}},
     journal = {Canadian mathematical bulletin},
     pages = {399--404},
     year = {1978},
     volume = {21},
     number = {4},
     doi = {10.4153/CMB-1978-070-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1978-070-x/}
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