Rings with associators in the commutative center
Proc. Amer. Math. Soc. 104 (1988), 10-12
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Abstract: Thedy has introduced the subject of rings which satisfy the identity where the commutator is defined by , and the associator is defined by and which satisfy one additional identity such as . Assuming characteristic and simplicity, Thedy's result is that such a ring must be either commutative or associative. Thedy also showed that simplicity could not be relaxed to prime by presenting some examples which are neither associative nor commutative. We show here that the additional identity assumed by Thedy is in fact unnecessary for we show that if is simple, characteristic and satisfies (I) then must be either commutative or associative.
- Erwin Kleinfeld, A class of rings which are very nearly associative, Amer. Math. Monthly 93 (1986), 720-722. MR 863975 (87j:17003)
- Armin Thedy, On rings satisfying , Proc. Amer. Math. Soc. 29 (1971), 213-218.
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