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

BRIEF MESSAGE

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
Received: 30.09.2019
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}


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