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. For 2 ≤ 6 s ≤ 5 we have that all a...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2003 |
| Автори: | , , , , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2003
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/155712 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-155712 |
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dspace |
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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 |
| 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. II |
| 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_short |
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_sort |
tiled orders over discrete valuation rings, finite markov chains and partially ordered sets. ii |
| 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 |
2003 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/155712 |
| 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. |
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