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

• Date: 2001
• Main Authors: Rabanovych, V. I., Samoilenko, Yu. S., Strilets, O. V., Рабанович, В. И., Самойленко, Ю. С., Стрелец, А. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2001
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4357
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 $Q_{4,2},\; λ ≠ 2$,...