On hereditary reducibility of 2-monomial matrices over commutative rings
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 companion matrix to \...
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| Date: | 2019 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2019
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1333 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | 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 companion 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. |
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