English

Local Centrally Essential Subalgebras of Triangular Algebras

Rings and Algebras 2020-07-27 v1

Abstract

We study local centrally essential subalgebras in the algebra of all upper triangular matrices over a field of characteristic 2\ne 2. It is proved that the algebras of upper triangular 3×33\times 3 or 4×44\times 4 matrices have only commutative local centrally essential subalgebras. Every algebra of upper triangular matrices of order exceeding 66 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.

Keywords

Cite

@article{arxiv.2007.12243,
  title  = {Local Centrally Essential Subalgebras of Triangular Algebras},
  author = {O. V. Lyubimtsev and A. A. Tuganbaev},
  journal= {arXiv preprint arXiv:2007.12243},
  year   = {2020}
}