2019
Том 71
№ 11

All Issues

On Identities in Algebras $Q_{n,λ}$ Generated by Idempotents

Rabanovych V. I., Samoilenko Yu. S., Strilets O. V.

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Abstract

We investigate the presence of polynomial identities in the algebras $Q_{n,λ}$ generated by $n$ idempotents with the sum $λe$ ($λ ∈ C$ and $e$ is the identity of an algebra). We prove that $Q_{4,2}$ is an algebra with the standard polynomial identity $F_4$, whereas the algebras $Q_{4,2},\; λ ≠ 2$, and $Q_{n,λ},\; n ≥ 5$, do not have polynomial identities.

English version (Springer): Ukrainian Mathematical Journal 53 (2001), no. 10, pp October 2001, Volume.

Citation Example: Rabanovych V. I., Samoilenko Yu. S., Strilets O. V. On Identities in Algebras $Q_{n,λ}$ Generated by Idempotents // Ukr. Mat. Zh. - 2001. - 53, № 10. - pp. 1380-1390.

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