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: | Англійська |
| Опубліковано: |
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 |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543027832553472 |
|---|---|
| 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. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2019-04-09T04:55:37Z |
| 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. |
| first_indexed | 2025-12-02T15:38:43Z |
| format | Article |
| id | admjournalluguniveduua-article-1333 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:38:43Z |
| publishDate | 2019 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| 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 |
| title | 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_short | On hereditary reducibility of 2-monomial matrices over commutative rings |
| title_sort | on hereditary reducibility of 2-monomial matrices over commutative rings |
| topic | commutative ring Jacobson radical 2-monomial matrix hereditary reducible matrix similarity linear operator free module 15B33 15A30 |
| topic_facet | commutative ring Jacobson radical 2-monomial matrix hereditary reducible matrix similarity linear operator free module 15B33 15A30 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1333 |
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