论文标题
三角形代数的局部本地必需的亚代数
Local Centrally Essential Subalgebras of Triangular Algebras
论文作者
论文摘要
我们研究了特征性$ \ ne 2 $的所有上三角矩阵的代数中的本地必不可少的子代数。事实证明，上三角形的代数$ 3 \ times 3 $或$ 4 \ times 4 $矩阵只有换向的本地中央基本亚词法。订单的上三角矩阵的每个代数都超过$ 6 $，都包含一个非交易性的当地中央基本亚词法。 该论文将以线性和多线性代数出现。 O.V.的工作lyubimtsev是在国家分配第〜0729-2020-0055下完成的。 A.A. Tuganbaev得到了俄罗斯科学基金会的支持，项目16-11-10013p。
We study local centrally essential subalgebras in the algebra of all upper triangular matrices over a field of characteristic $\ne 2$. It is proved that the algebras of upper triangular $3\times 3$ or $4\times 4$ 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.
