On rings satisfying [(𝑎,𝑏,𝑐),𝑑]=0

Thedy, Armin

doi:10.1090/S0002-9939-1971-0294432-4

On rings satisfying $[(a, b, c), d]=0$
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Proc. Amer. Math. Soc. 29 (1971), 250-254 Request permission

Abstract:

A simple nonassociative ring, in which the associators commute with all elements, is under mild additional assumptions either associative or commutative. This result cannot be extended to prime rings since a construction of semiprime rings gives counterexamples.

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