arXiv subjects

A. A. Tuganbaev

Publications and source records attributed to A. A. Tuganbaev.

2 recordsLinked to original sources

arXiv2023

$\aleph_0$-distributive modules and rings

Let $A$ be a ring with minimum condition on principal right ideals. It is proved that $\aleph_0$-distributive right (left) $A$-modules coincide with Artinian (Noetherian) right (left) $A$-modules. Rings, over which all right modules are direct sums of $\aleph_0$-distributive coincide with rings of of finite representation type. Rings, whose right modules are semidistributive, coincide with Kawada rings, over basis rings of which all right modules are completely cyclic. The studies of Tuganbaev are supported by Russian Scientific Foundation, project 22-11-00052.

math.RA↗

arXiv2020

Local Centrally Essential Subalgebras of Triangular Algebras

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.

math.RA↗