Complete classification of two classes of two-dimensional PI-algebras over any basic field; [Полная классификация двух классов двумерных PI-алгебр над любым основным полем]

• Published in: Chebyshevskii Sbornik
• Main Author: Sattarovich R.I.; Hakim J.; Narinie M.N.R.
• Format: Article
• Language: English
• Published: State Lev Tolstoy Pedagogical University 2024
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85217530746&doi=10.22405%2f2226-8383-2024-25-5-164-182&partnerID=40&md5=a70808d1ffea010d8623c5c75fd4190e

In the paper we give complete classification of two classes of two-dimensional PI-algebras over any basic field. The choice of these two classes is predicted by the polynomial identities of the classes: the identity of one of them is given by using the binary operation of the algebra another one involves the bracket operation in the identity. The list of the representatives of isomorphism classes are provided. We compare our list with that obtained earlier, where such a classification was given under certain constraints on the basic field. © 2024 State Lev Tolstoy Pedagogical University. All rights reserved.