Geodesic
On $T$-nilpotence of a matrix set
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2023), pp. 36-40

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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. 
@article{BASM_2023_2_a3,
     author = {Yu. P. Maturin},
     title = {On $T$-nilpotence of a matrix set},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {36--40},
     publisher = {mathdoc},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2023_2_a3/}
}
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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/