Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II
The main concept of this part of the paper is that of a reduced exponent matrix and its quiver, which is strongly connected and simply laced. We give the description of quivers of reduced Gorenstein exponent matrices whose number \(s\) of vertices is at most \(7\). For \(2\leq s\leq 5\) we have that...
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| Date: | 2018 |
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| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/958 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543369690349568 |
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| 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. |
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| collection | OJS |
| datestamp_date | 2018-05-13T07:14:40Z |
| description | The main concept of this part of the paper is that of a reduced exponent matrix and its quiver, which is strongly connected and simply laced. We give the description of quivers of reduced Gorenstein exponent matrices whose number \(s\) of vertices is at most \(7\). For \(2\leq s\leq 5\) we have that all adjacency matrices of such quivers are multiples of doubly stochastic matrices. We prove that for any permutation \(\sigma \) on \(n\) letters without fixed elements there exists a reduced Gorenstein tiled order \(\Lambda\) with \(\sigma ({\mathcal{E}})=\sigma\). We show that for any positive integer \(k\) there exists a Gorenstein tiled order \(\Lambda_{k}\) with \(in\Lambda_{k}=k\). The adjacency matrix of any cyclic Gorenstein order \(\Lambda \) is a linear combination of powers of a permutation matrix \(P_{\sigma}\) with non-negative coefficients, where \(\sigma = \sigma(\Lambda)\). If \(A\) is a noetherian prime semiperfect semidistributive ring of a finite global dimension, then \(Q(A)\) be a strongly connected simply laced quiver which has no loops. |
| first_indexed | 2026-02-08T08:02:08Z |
| format | Article |
| id | admjournalluguniveduua-article-958 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:02:08Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-9582018-05-13T07:14:40Z Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II Chernousova, Zh. T. Dokuchaev, M. A. Khibina, M. A. Kirichenko, V. V. Miroshnichenko, S. G. Zhuravlev, V. N. semiperfect ring, exponent matrix, tiled order, quiver, partially ordered set, index of semiperfect ring, Gorenstein tiled order, global dimension, transition matrix 16P40, 16G10 The main concept of this part of the paper is that of a reduced exponent matrix and its quiver, which is strongly connected and simply laced. We give the description of quivers of reduced Gorenstein exponent matrices whose number \(s\) of vertices is at most \(7\). For \(2\leq s\leq 5\) we have that all adjacency matrices of such quivers are multiples of doubly stochastic matrices. We prove that for any permutation \(\sigma \) on \(n\) letters without fixed elements there exists a reduced Gorenstein tiled order \(\Lambda\) with \(\sigma ({\mathcal{E}})=\sigma\). We show that for any positive integer \(k\) there exists a Gorenstein tiled order \(\Lambda_{k}\) with \(in\Lambda_{k}=k\). The adjacency matrix of any cyclic Gorenstein order \(\Lambda \) is a linear combination of powers of a permutation matrix \(P_{\sigma}\) with non-negative coefficients, where \(\sigma = \sigma(\Lambda)\). If \(A\) is a noetherian prime semiperfect semidistributive ring of a finite global dimension, then \(Q(A)\) be a strongly connected simply laced quiver which has no loops. Lugansk National Taras Shevchenko University 2018-05-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/958 Algebra and Discrete Mathematics; Vol 2, No 2 (2003) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/958/487 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | semiperfect ring exponent matrix tiled order quiver partially ordered set index of semiperfect ring Gorenstein tiled order global dimension transition matrix 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. II |
| title | Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II |
| title_full | Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II |
| title_fullStr | Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II |
| title_full_unstemmed | Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II |
| title_short | Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II |
| title_sort | tiled orders over discrete valuation rings, finite markov chains and partially ordered sets. ii |
| topic | semiperfect ring exponent matrix tiled order quiver partially ordered set index of semiperfect ring Gorenstein tiled order global dimension transition matrix 16P40 16G10 |
| topic_facet | semiperfect ring exponent matrix tiled order quiver partially ordered set index of semiperfect ring Gorenstein tiled order global dimension transition matrix 16P40 16G10 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/958 |
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