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-v...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2002 |
| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2002
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| Zitieren: | 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| _version_ | 1862715655617249280 |
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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. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T17:59:38Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155280 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T17:59:38Z |
| publishDate | 2002 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| 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 | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155280 |
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