Geodesic
On $T$-nilpotence of a matrix set
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2023), pp. 36-40 
Yu. P. Maturin. On $T$-nilpotence of a matrix set. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2023), pp. 36-40. http://geodesic.mathdoc.fr/item/BASM_2023_2_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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