Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I
We prove that the quiver of tiled order over a discrete valuation ring is strongly connected and simply laced. With such quiver we associate a finite ergodic Markov chain. We introduce the notion of the index \(in\,A\) of a right noetherian semiperfect ring \(A\) as the maximal real eigen-value of i...
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| Дата: | 2018 |
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| Автори: | , , , , , |
| Формат: | Стаття |
| Мова: | Англійська |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/3 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543431300481024 |
|---|---|
| author | Chernousova, Zh. T. Dokuchaev, M. A. Khibina, M. A. Kirichenko, V. V. Miroshnichenko, S. G. Zhuravlev, V. N. |
| author_facet | Chernousova, Zh. T. Dokuchaev, M. A. Khibina, M. A. Kirichenko, V. V. Miroshnichenko, S. G. Zhuravlev, V. N. |
| author_sort | Chernousova, Zh. T. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-05-15T14:22:44Z |
| description | We prove that the quiver of tiled order over a discrete valuation ring is strongly connected and simply laced. With such quiver we associate a finite ergodic Markov chain. We introduce the notion of the index \(in\,A\) of a right noetherian semiperfect ring \(A\) as the maximal real eigen-value of its adjacency matrix. A tiled order \(\Lambda \) is integral if \(in\,\Lambda\) is an integer. Every cyclic Gorenstein tiled order is integral. In particular, \(in\, \Lambda\,=\,1\) if and only if \(\Lambda\) is hereditary. We give an example of a non-integral Gorenstein tiled order. We prove that a reduced \((0, 1)\)-order is Gorenstein if and only if either\(in\,\Lambda\,=\,w(\Lambda )\,=\,1\), or \(in\,\Lambda\,=\,w(\Lambda )\,=\,2\), where \(w(\Lambda )\) is a width of \(\Lambda \). |
| first_indexed | 2025-12-02T15:42:47Z |
| format | Article |
| id | admjournalluguniveduua-article-3 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:42:47Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-32018-05-15T14:22:44Z Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I Chernousova, Zh. T. Dokuchaev, M. A. Khibina, M. A. Kirichenko, V. V. Miroshnichenko, S. G. Zhuravlev, V. N. emiperfect ring, tiled order, quiver, partially ordered set, index of semiperfect ring, Gorenstein tiled order, finite Markov chain 16P40, 16G10 We prove that the quiver of tiled order over a discrete valuation ring is strongly connected and simply laced. With such quiver we associate a finite ergodic Markov chain. We introduce the notion of the index \(in\,A\) of a right noetherian semiperfect ring \(A\) as the maximal real eigen-value of its adjacency matrix. A tiled order \(\Lambda \) is integral if \(in\,\Lambda\) is an integer. Every cyclic Gorenstein tiled order is integral. In particular, \(in\, \Lambda\,=\,1\) if and only if \(\Lambda\) is hereditary. We give an example of a non-integral Gorenstein tiled order. We prove that a reduced \((0, 1)\)-order is Gorenstein if and only if either\(in\,\Lambda\,=\,w(\Lambda )\,=\,1\), or \(in\,\Lambda\,=\,w(\Lambda )\,=\,2\), where \(w(\Lambda )\) is a width of \(\Lambda \). Lugansk National Taras Shevchenko University 2018-05-15 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/3 Algebra and Discrete Mathematics; Vol 1, No 1 (2002) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/3/4 Copyright (c) 2015 Algebra and Discrete Mathematics |
| spellingShingle | emiperfect ring tiled order quiver partially ordered set index of semiperfect ring Gorenstein tiled order finite Markov chain 16P40 16G10 Chernousova, Zh. T. Dokuchaev, M. A. Khibina, M. A. Kirichenko, V. V. Miroshnichenko, S. G. Zhuravlev, V. N. Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I |
| title | Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I |
| title_full | Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I |
| title_fullStr | Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I |
| title_full_unstemmed | Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I |
| title_short | Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I |
| title_sort | tiled orders over discrete valuation rings, finite markov chains and partially ordered sets. i |
| topic | emiperfect ring tiled order quiver partially ordered set index of semiperfect ring Gorenstein tiled order finite Markov chain 16P40 16G10 |
| topic_facet | emiperfect ring tiled order quiver partially ordered set index of semiperfect ring Gorenstein tiled order finite Markov chain 16P40 16G10 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/3 |
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