http://dspace.nbuv.gov.ua:80/handle/123456789/150324 Mon, 20 Apr 2026 23:03:12 GMT 2026-04-20T23:03:12Z http://dspace.nbuv.gov.ua:80/bitstream/id/448071/ http://dspace.nbuv.gov.ua:80/handle/123456789/150324 http://dspace.nbuv.gov.ua:80/handle/123456789/157658 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. Tue, 01 Jan 2002 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/157658 2002-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155283 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. Tue, 01 Jan 2002 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/155283 2002-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155280 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. Tue, 01 Jan 2002 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/155280 2002-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155217 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. Tue, 01 Jan 2002 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/155217 2002-01-01T00:00:00Z