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

  • V. I. Rabanovych
  • Yu. S. Samoilenko Iн-т математики НАН України, Київ
  • O. V. Strilets


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.
How to Cite
Rabanovych, V. I., Y. S. Samoilenko, and O. V. Strilets. “On Identities in Algebras $Q_{n,λ}$ Generated by Idempotents”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 53, no. 10, Oct. 2001, pp. 1380-9, https://umj.imath.kiev.ua/index.php/umj/article/view/4357.
Research articles