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On the identities in algebras generated by linearly connected idempotents

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Abstract

We investigate the problem of the existence of polynomial identities (PI) in algebras generated by idempotents whose linear combination is equal to identity. In the case where the number of idempotents is greater than or equal to five, we prove that these algebras are not PI-algebras. In the case of four idempotents, in order that an algebra be a PI-algebra, it is necessary and sufficient that the sum of the coefficients of the linear combination be equal to two. In this case, these algebras are F 4-algebras.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    V. I. Rabanovich, Yu. S. Samoilenko & A. V. Strelets

Authors
  1. V. I. Rabanovich
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  2. Yu. S. Samoilenko
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  3. A. V. Strelets
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 6, pp. 782–795, June, 2004.

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Rabanovich, V.I., Samoilenko, Y.S. & Strelets, A.V. On the identities in algebras generated by linearly connected idempotents. Ukr Math J 56, 929–946 (2004). https://doi.org/10.1007/PL00022181

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  • DOI: https://doi.org/10.1007/PL00022181

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