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

• Published in: Algebra and Discrete Mathematics
• Date: 2002
• Main Authors: Chernousova, Zh.T., Dokuchaev, M.A., Khibina, M.A., Kirichenko, V.V., Miroshnichenko, S.G., Zhuravlev, V.N.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2002
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/155280
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I / Zh.T. Chernousova, M.A. Dokuchaev, M.A. Khibina, V.V. Kirichenko, S.G. Miroshnichenko, V.N. Zhuravlev // Algebra and Discrete Mathematics. — 2002. — Vol. 1, № 1. — С. 32–63. — назв. — англ.

We prove that the quiver of tiled order over a discrete valuation ring is strongly connected and simply laced. With such quiver we associate a finite ergodic Markov chain. We introduce the notion of the index in A of a right noetherian semiperfect ring A as the maximal real eigen-value of its adja...