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 paper will appear in Linear and Multilinear Algebra. 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.
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