On $T$-nilpotence of a matrix set

Yu. P. Maturin

Department of Mathematics and Economics, Faculty of Physics, Mathematics, Economics and Innovation Technologies, Drohobych Ivan Franko State Pedagogical University, Stryiska Str., 3, Drohobych, 82100, Lviv Region, Ukraine

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 $n\times n$-matrices with entries in $I$ is a right $T$-nilpotent subset of the ring of $n\times n$-matrices with entries in $R$, where $n\in {\mathbb N}$. It is also showed that it is impossible to generalize this result for rings of matrices of infinite dimension.

Keywords and phrases: $T$-nilpotent, matrix, ring.

MSC: 16D99, 16D90

Received: 18.09.2022

Language: English

DOI: 10.56415/basm.y2023.i2.p36