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. 
@article{CHEB_2019_20_3_a27,
     author = {P. V. Danchev},
     title = {On a property of nilpotent matrices over an algebraically closed field},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {401--404},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2019_20_3_a27/}
}
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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/