Abstract
We investigate the presence of polynomial identities in the algebras Qn,λ generated by n idempotents with the sum λe (λ∈\({\mathbb{C}}\) and e is the identity of an algebra). We prove that Q4,2 is an algebra with the standard polynomial identity F4, whereas the algebras Q4,λ, λ ≠ 2, and Qn,λ, n ≥ 5, do not have polynomial identities.
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