On T-nilpotence of a matrix set

descriptionPublicationkeyboard_double_arrow_right Article 01 Nov 2023Publisher:Moldova State UniversityJournal:Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica (issn: 1024-7696, eissn: 2587-4322,

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Authors: Yuriy Maturin;

doi: 10.56415/basm.y2023.i2.p36

On T-nilpotence of a matrix set

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Abstract

Let R be a ring and I be an arbitrary right T-nilpotent subset of R. In the paper it is proved that in this case the set of all n×n-matrices with entries in I is a right T-nilpotent subset of the ring of n×n-matrices with entries in R, where n 2 N. It is also showed that it is impossible to generalize this result for rings of matrices of infinite dimension.

Related Organizations

Zhytomyr Ivan Franko State University
Ukraine

Keywords

\(T\)-nilpotent, Module categories in associative algebras, Torsion theories; radicals on module categories (associative algebraic aspects), matrix, ring

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