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Algebra and Discrete Mathematics, 2013, Volume 16, Issue 2, Pages 171–187
(Mi adm445)
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This article is cited in 4 scientific papers (total in 4 papers)
RESEARCH ARTICLE
Reducibility and irreducibility of monomial matrices over commutative rings
V. M. Bondarenkoa, M. Yu. Bortosb, R. F. Dinisc, A. A. Tylyshchakb a Institute of Mathematics, Tereshchenkivska 3, 01601 Kyiv, Ukraine
b Faculty of Mathematics, Uzhgorod National Univ., Universytetsyka str., 14, 88000 Uzhgorod, Ukraine
c Faculty of Mechanics and Mathematics, Kyiv National Taras Shevchenko Univ., Volodymyrska str., 64, 01033 Kyiv, Ukraine
Abstract:
Let $R$ be a local ring with nonzero Jacobson radical.
We study monomial matrices over $R$ of the form
$$
\left(
\begin{smallmatrix}
0&\ldots&0&t^{s_n}\\
t^{s_1}&\ldots&0&0\\
\vdots&\ddots&\vdots&\vdots\\
0&\ldots&t^{s_{n-1}}&0\\
\end{smallmatrix}
\right),
$$
and give a criterion for such matrices to be reducible when $n\leq 6$, $s_1\ldots,s_n\in\{0,1\}$
and the radical is a principal ideal with generator $t$.
We also show that the criterion does not hold for $n=7$.
Keywords:
irreducible matrix, similarity, local ring, Jacobson radical.
Received: 20.10.2013 Revised: 20.10.2013
Citation:
V. M. Bondarenko, M. Yu. Bortos, R. F. Dinis, A. A. Tylyshchak, “Reducibility and irreducibility of monomial matrices over commutative rings”, Algebra Discrete Math., 16:2 (2013), 171–187
Linking options:
https://www.mathnet.ru/eng/adm445 https://www.mathnet.ru/eng/adm/v16/i2/p171
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