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

• 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
• Series: Algebra and Discrete Mathematics
• Online Access: http://dspace.nbuv.gov.ua/handle/123456789/155280

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...