Abstract
It is proved that the identities ([x, y]4, z, t) = ([x, y]2, z, t) [x, y] = [x, y] ([x, y]2, z, t) = 0, known in the theory of alternative rings as the Kleinfeld identities, are fulfilled in every generalized accessible ring of characteristic different from 2 and 3. These identities allow us to construct central and kernel functions in the variety of generalized accessible rings. It is also proved that in a free generalized accessible and a free alternative ring with more than three generators the Kleinfeld element ([x, y]2, z, t) is nilpotent of index 2.
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Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 291–297, February, 1976.
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Dorofeev, G.V. The Kleinfeld identities in generalized accessible rings. Mathematical Notes of the Academy of Sciences of the USSR 19, 172–175 (1976). https://doi.org/10.1007/BF01098752
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DOI: https://doi.org/10.1007/BF01098752