We deal with adjoint commutator and Jordan algebras of isotopes of prime strictly (−1, 1)-algebras. It is proved that a system of identities of the form [x 1, x 2, x 2, x 3,…, x n ] for n = 2,.…, 5 is discernible on isotopes of prime (−1, 1)-algebras. Also it is shown that adjoint Jordan algebras for suitable isotopes of prime (−1, 1)-algebras may possess distinct sets of identities. In particular, isotopes of a prime Jordan monster have different sets of identities in general.
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Translated from Algebra i Logika, Vol. 49, No. 3, pp. 388–423, May–June, 2010.
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Pchelintsev, S.V. Isotopes of prime (−1, 1)-and Jordan algebras. Algebra Logic 49, 262–288 (2010). https://doi.org/10.1007/s10469-010-9095-4
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DOI: https://doi.org/10.1007/s10469-010-9095-4