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. Fo...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2003 |
| Main Authors: | , , , , , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2003
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155712 |
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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. II / Zh.T. Chernousova, M.A. Dokuchaev, M.A. Khibina, V.V. Kirichenko, S.G. Miroshnichenko, V.N. Zhuravlev // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 2. — С. 47–86. — Бібліогр.: 44 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862667768893014016 |
|---|---|
| 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. II / Zh.T. Chernousova, M.A. Dokuchaev, M.A. Khibina, V.V. Kirichenko, S.G. Miroshnichenko, V.N. Zhuravlev // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 2. — С. 47–86. — Бібліогр.: 44 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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 ≤ 6 s ≤ 5 we have that all adjacency matrices of
such quivers are multiples of doubly stochastic matrices. We prove
that for any permutation σ on n letters without fixed elements
there exists a reduced Gorenstein tiled order Λ with σ(ε) = σ.
We show that for any positive integer k there exists a Gorenstein
tiled order Λk with inΛk = k. The adjacency matrix of any cyclic
Gorenstein order Λ is a linear combination of powers of a permutation matrix Pσ with non-negative coefficients, where σ = σ(Λ).
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 | 2025-12-07T15:23:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155712 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T15:23:15Z |
| publishDate | 2003 |
| 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. 2019-06-17T11:08:34Z 2019-06-17T11:08:34Z 2003 Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II / Zh.T. Chernousova, M.A. Dokuchaev, M.A. Khibina, V.V. Kirichenko, S.G. Miroshnichenko, V.N. Zhuravlev // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 2. — С. 47–86. — Бібліогр.: 44 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 16P40, 16G10. https://nasplib.isofts.kiev.ua/handle/123456789/155712 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 ≤ 6 s ≤ 5 we have that all adjacency matrices of
 such quivers are multiples of doubly stochastic matrices. We prove
 that for any permutation σ on n letters without fixed elements
 there exists a reduced Gorenstein tiled order Λ with σ(ε) = σ.
 We show that for any positive integer k there exists a Gorenstein
 tiled order Λk with inΛk = k. The adjacency matrix of any cyclic
 Gorenstein order Λ is a linear combination of powers of a permutation matrix Pσ with non-negative coefficients, where σ = σ(Λ).
 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. 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. II Article published earlier |
| spellingShingle | 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. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155712 |
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