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 Chebyshevskii Sb., 2019, Volume 20, Issue 3, Pages 401–404 (Mi cheb821)

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On a property of nilpotent matrices over an algebraically closed field

P. V. Danchev

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (Sofia, Bulgaria)

Abstract: 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.

DOI: https://doi.org/10.22405/2226-8383-2018-20-3-401-404

Full text: PDF file (573 kB)

MSC: 16U99, 16E50, 16W10, 13B99
Accepted:12.11.2019
Language:

Citation: P. V. Danchev, “On a property of nilpotent matrices over an algebraically closed field”, Chebyshevskii Sb., 20:3 (2019), 401–404

Citation in format AMSBIB
\Bibitem{Dan19} \by P.~V.~Danchev \paper On a property of nilpotent matrices over an algebraically closed field \jour Chebyshevskii Sb. \yr 2019 \vol 20 \issue 3 \pages 401--404 \mathnet{http://mi.mathnet.ru/cheb821} \crossref{https://doi.org/10.22405/2226-8383-2018-20-3-401-404}