Geodesic
On a property of nilpotent matrices over an algebraically closed field
Čebyševskij sbornik, Tome 20 (2019) no. 3, pp. 401-404.

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Suppose $F$ is an algebraically closed field. We prove that the ring $\prod_{n=1}^\infty \mathbb M_n(F)$ has a special property which is, somewhat, in sharp parallel with (and slightly better than) a property established by Šter (LAA, 2018) for the rings $\prod_{n=1}^\infty \mathbb M_n(\mathbb Z_2)$ and $\prod_{n=1}^\infty \mathbb M_n(\mathbb Z_4)$, where $\mathbb Z_2$ is the finite simple field of two elements and $\mathbb Z_4$ is the finite indecomposable ring of four elements.
Keywords: nilpotent matrices, idempotent matrices, Jordan canonical form, algebraically closed fields. 
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     title = {On a property of nilpotent matrices over an algebraically closed field},
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P. V. Danchev. On a property of nilpotent matrices over an algebraically closed field. Čebyševskij sbornik, Tome 20 (2019) no. 3, pp. 401-404. http://geodesic.mathdoc.fr/item/CHEB_2019_20_3_a27/

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