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

Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/60

Title:	Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II
Authors:	Chernousova, Zh.T. Dokuchaev, M.A. Khibina, M.A. Kirichenko, V.V. Miroshnichenko, S.G. Zhuravlev, V.N.
Issue Date:	28-Mar-2003
Publisher:	Луганский национальный университет им. Т. Шевченко
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 6 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 ¤ with σ(E) = σ. We show that for any positive integer k there exists a Gorenstein tiled order ¤k with in¤k = k. The adjacency matrix of any cyclic Gorenstein order ¤ is a linear combination of powers of a permutation matrix P¾ with non-negative coefficients, where σ = σ(¤). 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.
URI:	http://hdl.handle.net/123456789/60
Appears in Collections:	Статті

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