Local Centrally Essential Subalgebras of Triangular Algebras

Abstract

We study local centrally essential subalgebras in the algebra of all upper triangular matrices over a field of characteristic = 2. It is proved that the algebras of upper triangular 3 × 3 or 4 × 4 matrices have only commutative local centrally essential subalgebras. Every algebra of upper triangular matrices of order exceeding 6 contains a non-commutative local centrally essential subalgebra. The work of O.V. Lyubimtsev is done under the state assignment No 0729-2020-0055. A.A. Tuganbaev is supported by Russian Scientific Foundation, project 16-11-10013P. MSC2010 database 16R99; 20K30 1 Not necessarily unital rings with ( * ) are considered in [13].