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On hereditary reducibility of 2-monomial matrices over commutative rings
Bondarenko, Vitaliy M. Gildea, Joe Tylyshchak, Alexander Yurchenko, Natalia
Bondarenko, Vitaliy M.
Gildea, Joe
Tylyshchak, Alexander
Yurchenko, Natalia
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2019
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Abstract
A 2-monomial matrix over a commutative ring $R$ is by definition any matrix of the form $M(t,k,n)=\Phi\left(\begin{smallmatrix}I_k&0\\0&tI_{n-k}\end{smallmatrix}\right)$, $0<k<n$,
where $t$ is a non-invertible element of $R$, $\Phi$ the compa\-nion matrix to $\lambda^n-1$ and
$I_k$ the identity $k\times k$-matrix. In this paper we introduce the notion of hereditary reducibility (for these matrices) and indicate one general condition of the introduced reducibility.
Citation
Bondarenko, V. M., Gildea, J., Tylyshchak, A. A., & Yurchenko, N. V. (2019). On hereditary reducibility of 2-monomial matrices over commutative rings. Algebra and Discrete Mathematics, 27(1).
Publisher
Taras Shevchenko National University of Luhansk
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Algebra and Discrete Mathematics
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Article
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en
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ISSN
1726-3255
EISSN
2415-721X