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Algebra and Discrete Mathematics, 2003, выпуск 2, страницы 47–86
(Mi adm378)
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Эта публикация цитируется в 6 научных статьях (всего в 6 статьях)
RESEARCH ARTICLE
Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II
Zh. T. Chernousovaa, M. A. Dokuchaevb, M. A. Khibinac, V. V. Kirichenkoa, S. G. Miroshnichenkoa, V. N. Zhuravleva a Faculty of Mechanics and Mathematics, Kiev
National Taras Shevchenko Univ., Vladimirskaya Str., 64, Kiev,
Ukraine
b Departamento de Matematica Univ. de Sao
Paulo, Caixa Postal 66281, Sao Paulo, SP,
05315–970 — Brazil
c Glushkov In-t of Cybernetics NAS Ukraine,
Glushkov Av., 40, 03680 Kiev, Ukraine
Аннотация:
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.
Ключевые слова:
semiperfect ring, exponent matrix, tiled order, quiver, partially ordered set, index of semiperfect ring, Gorenstein tiled order, global dimension, transition matrix.
Поступила в редакцию: 28.03.2003 Исправленный вариант: 03.07.2003
Образец цитирования:
Zh. T. Chernousova, M. A. Dokuchaev, M. A. Khibina, V. V. Kirichenko, S. G. Miroshnichenko, V. N. Zhuravlev, “Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II”, Algebra Discrete Math., 2003, no. 2, 47–86
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm378 https://www.mathnet.ru/rus/adm/y2003/i2/p47
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Страница аннотации: | 139 | PDF полного текста: | 64 | Первая страница: | 1 |
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