On the identities in algebras generated by linearly connected idempotents

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


We investigate the problem of the existence of polynomial identities (PI) in algebras generated by idempotents whose linear combination is equal to identity. In the case where the number of idempotents is greater than or equal to five, we prove that these algebras are not PI-algebras. In the case of four idempotents, in order that an algebra be a PI-algebra, it is necessary and sufficient that the sum of the coefficients of the linear combination be equal to two. In this case, these algebras are F 4-algebras.
How to Cite
Rabanovych, V. I., Y. S. Samoilenko, and O. V. Strilets. “On the Identities in Algebras Generated by Linearly Connected Idempotents”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 6, June 2004, pp. 782–795, https://umj.imath.kiev.ua/index.php/umj/article/view/3798.
Research articles