Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II
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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 |
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. |
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| Date |
2019-06-17T11:08:34Z
2019-06-17T11:08:34Z 2003 |
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| Type |
Article
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| Identifier |
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. http://dspace.nbuv.gov.ua/handle/123456789/155712 |
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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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