Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I
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| Creator |
Chernousova, Zh.T.
Dokuchaev, M.A. Khibina, M.A. Kirichenko, V.V. Miroshnichenko, S.G. Zhuravlev, V.N. |
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| 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. |
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| Date |
2019-06-16T15:30:26Z
2019-06-16T15:30:26Z 2002 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/155280 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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