Algebra and Discrete Mathematics, 2002, № 1 http://dspace.nbuv.gov.ua:80/handle/123456789/150324 2026-04-20T23:05:32Z 2026-04-20T23:05:32Z Metrizable ball structures Protasov, I.V. http://dspace.nbuv.gov.ua:80/handle/123456789/157658 2019-06-20T22:26:05Z 2002-01-01T00:00:00Z Metrizable ball structures Protasov, I.V. A ball structure is a triple (X, P, B), where X, P are nonempty sets and, for any x ∈ X, α ∈ P, B(x, α) is a subset of X, x ∈ B(x, α), which is called a ball of radius α around x. We characterize up to isomorphism the ball structures related to the metric spaces of different types and groups. 2002-01-01T00:00:00Z On dispersing representations of quivers and their connection with representations of bundles of semichains Bondarenko, V.M. http://dspace.nbuv.gov.ua:80/handle/123456789/155283 2019-06-16T22:27:04Z 2002-01-01T00:00:00Z On dispersing representations of quivers and their connection with representations of bundles of semichains Bondarenko, V.M. In the paper we discuss the notion of “dispersing representation of a quiver” and give, in a natural special case, a criterion for the problem of classifying such representations to be tame. In proving the criterion we essentially use representations of bundles of semichains, introduced about fifteen years ago by the author. 2002-01-01T00:00:00Z Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I Chernousova, Zh.T. Dokuchaev, M.A. Khibina, M.A. Kirichenko, V.V. Miroshnichenko, S.G. Zhuravlev, V.N. http://dspace.nbuv.gov.ua:80/handle/123456789/155280 2019-06-16T22:31:53Z 2002-01-01T00:00:00Z Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I Chernousova, Zh.T.; Dokuchaev, M.A.; Khibina, M.A.; Kirichenko, V.V.; Miroshnichenko, S.G.; Zhuravlev, V.N. 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 adjacency matrix. A tiled order Λ is integral if in Λ is an integer. Every cyclic Gorenstein tiled order is integral. In particular, in Λ = 1 if and only if Λ is hereditary. We give an example of a non-integral Gorenstein tiled order. We prove that a reduced (0, 1)-order is Gorenstein if and only if either inΛ = w(Λ) = 1, or inΛ = w(Λ) = 2, where w(Λ) is a width of Λ. 2002-01-01T00:00:00Z On groups of finite normal rank Dashkova, O.Yu. http://dspace.nbuv.gov.ua:80/handle/123456789/155217 2019-06-16T22:30:58Z 2002-01-01T00:00:00Z On groups of finite normal rank Dashkova, O.Yu. In this article the investigation of groups of finite normal rank is continued. The finiteness of normal rank of nonabelian p-group G is proved where G has a normal elementary abelian p-subgroup A for which quotient group G/A is isomorphic to the direct product of finite number of quasicyclic p-groups. 2002-01-01T00:00:00Z