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Basis for identities of the algebra of simplified insertion

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Abstract

We prove that all identities of the algebra of simplified insertion on countably many generators over a field of characteristic zero follow from the right-symmetric identity. We prove that the bases of the free special Jordan algebra and the special algebra of simplified insertion coincide. We construct an infinite series of relations in the algebra of simplified insertion which hold for the words of length k, k ε ℕ.

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Correspondence to S. R. Sverchkov.

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Original Russian Text Copyright © 2009 Sverchkov S. R.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 6, pp. 1384–1390, November–December, 2009.

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Sverchkov, S.R. Basis for identities of the algebra of simplified insertion. Sib Math J 50, 1092–1097 (2009). https://doi.org/10.1007/s11202-009-0120-6

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  • DOI: https://doi.org/10.1007/s11202-009-0120-6

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