Abstract
We investigate the presence of polynomial identities in the algebras Q n,λ generated by n idempotents with the sum λe (λ∈\({\mathbb{C}}\) 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,λ, λ ≠ 2, and Q n,λ, n ≥ 5, do not have polynomial identities.
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Rabanovich, V.I., Samoilenko, Y.S. & Strelets, A.V. On Identities in Algebras Q n,λ Generated by Idempotents. Ukrainian Mathematical Journal 53, 1673–1687 (2001). https://doi.org/10.1023/A:1015295927440
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DOI: https://doi.org/10.1023/A:1015295927440