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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| Дата: | 2019 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2019
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1333 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-13332019-04-09T04:55:37Z On hereditary reducibility of 2-monomial matrices over commutative rings Bondarenko, Vitaliy M. Gildea, Joseph Tylyshchak, Alexander A. Yurchenko, Natalia V. commutative ring, Jacobson radical, 2-monomial matrix, hereditary reducible matrix, similarity, linear operator, free module 15B33, 15A30 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. Lugansk National Taras Shevchenko University 2019-03-23 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1333 Algebra and Discrete Mathematics; Vol 27, No 1 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1333/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1333/499 Copyright (c) 2019 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2019-04-09T04:55:37Z |
| collection |
OJS |
| language |
English |
| topic |
commutative ring Jacobson radical 2-monomial matrix hereditary reducible matrix similarity linear operator free module 15B33 15A30 |
| spellingShingle |
commutative ring Jacobson radical 2-monomial matrix hereditary reducible matrix similarity linear operator free module 15B33 15A30 Bondarenko, Vitaliy M. Gildea, Joseph Tylyshchak, Alexander A. Yurchenko, Natalia V. On hereditary reducibility of 2-monomial matrices over commutative rings |
| topic_facet |
commutative ring Jacobson radical 2-monomial matrix hereditary reducible matrix similarity linear operator free module 15B33 15A30 |
| format |
Article |
| author |
Bondarenko, Vitaliy M. Gildea, Joseph Tylyshchak, Alexander A. Yurchenko, Natalia V. |
| author_facet |
Bondarenko, Vitaliy M. Gildea, Joseph Tylyshchak, Alexander A. Yurchenko, Natalia V. |
| author_sort |
Bondarenko, Vitaliy M. |
| title |
On hereditary reducibility of 2-monomial matrices over commutative rings |
| title_short |
On hereditary reducibility of 2-monomial matrices over commutative rings |
| title_full |
On hereditary reducibility of 2-monomial matrices over commutative rings |
| title_fullStr |
On hereditary reducibility of 2-monomial matrices over commutative rings |
| title_full_unstemmed |
On hereditary reducibility of 2-monomial matrices over commutative rings |
| title_sort |
on hereditary reducibility of 2-monomial matrices over commutative rings |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2019 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1333 |
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2025-07-17T10:34:15Z |
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