Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II

• Опубліковано в: : Algebra and Discrete Mathematics
• Дата: 2003
• Автори: Chernousova, Zh.T., Dokuchaev, M.A., Khibina, M.A., Kirichenko, V.V., Miroshnichenko, S.G., Zhuravlev, V.N.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут прикладної математики і механіки НАН України 2003
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/155712
• 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.

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.