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 its adja...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2002 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2002
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155280 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I / Zh.T. Chernousova, M.A. Dokuchaev, M.A. Khibina, V.V. Kirichenko, S.G. Miroshnichenko, V.N. Zhuravlev // Algebra and Discrete Mathematics. — 2002. — Vol. 1, № 1. — С. 32–63. — назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Chernousova, Zh.T. Dokuchaev, M.A. Khibina, M.A. Kirichenko, V.V. Miroshnichenko, S.G. Zhuravlev, V.N. 2019-06-16T15:30:26Z 2019-06-16T15:30:26Z 2002 Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I / Zh.T. Chernousova, M.A. Dokuchaev, M.A. Khibina, V.V. Kirichenko, S.G. Miroshnichenko, V.N. Zhuravlev // Algebra and Discrete Mathematics. — 2002. — Vol. 1, № 1. — С. 32–63. — назв. — англ. 1726-3255 https://nasplib.isofts.kiev.ua/handle/123456789/155280 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 Λ is integral if in Λ is an integer. Every cyclic Gorenstein tiled order is integral. In particular, in Λ = 1 if and only if Λ 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 inΛ = w(Λ) = 1, or inΛ = w(Λ) = 2, where w(Λ) is a width of Λ. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I |
| spellingShingle |
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. |
| title_short |
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_sort |
tiled orders over discrete valuation rings, finite markov chains and partially ordered sets. i |
| 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. |
| publishDate |
2002 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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 Λ is integral if in Λ is an integer. Every cyclic Gorenstein tiled order is integral. In particular, in Λ = 1 if and only if
Λ 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 inΛ = w(Λ) = 1, or inΛ = w(Λ) = 2, where
w(Λ) is a width of Λ.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/155280 |
| citation_txt |
Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I / Zh.T. Chernousova, M.A. Dokuchaev, M.A. Khibina, V.V. Kirichenko, S.G. Miroshnichenko, V.N. Zhuravlev // Algebra and Discrete Mathematics. — 2002. — Vol. 1, № 1. — С. 32–63. — назв. — англ. |
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2025-12-07T17:59:38Z |
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