Digital Repository of Luhansk Taras Shevchenko National University
Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II
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| dc.contributor.author | Chernousova, Zh.T. | |
| dc.contributor.author | Dokuchaev, M.A. | |
| dc.contributor.author | Khibina, M.A. | |
| dc.contributor.author | Kirichenko, V.V. | |
| dc.contributor.author | Miroshnichenko, S.G. | |
| dc.contributor.author | Zhuravlev, V.N. | |
| dc.date.accessioned | 2015-10-20T11:27:56Z | |
| dc.date.available | 2015-10-20T11:27:56Z | |
| dc.date.issued | 2003-03-28 | |
| dc.identifier.uri | http://hdl.handle.net/123456789/60 | |
| dc.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. | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | Луганский национальный университет им. Т. Шевченко | uk_UA |
| dc.title | Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II | uk_UA |
| dc.type | Article | uk_UA |
