Algebra and Discrete Mathematics, 2003, № 1 http://dspace.nbuv.gov.ua:80/handle/123456789/150326 2026-04-18T13:46:46Z 2026-04-18T13:46:46Z Uniform ball structures Protasov, I.V. http://dspace.nbuv.gov.ua:80/handle/123456789/155285 2019-06-16T22:28:54Z 2003-01-01T00:00:00Z Uniform ball structures Protasov, I.V. A ball structure is a triple B = (X, P, B), where X, P are nonempty sets and, for all 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 introduce the class of uniform ball structures as an asymptotic counterpart of the class of uniform topological spaces. We show that every uniform ball structure can be approximated by metrizable ball structures. We also define two types of ball structures closed to being metrizable, and describe the extremal elements in the classes of ball structures with fixed support X. 2003-01-01T00:00:00Z Principal quasi-ideals of cohomological dimension 1 Novikov, B.V. http://dspace.nbuv.gov.ua:80/handle/123456789/155284 2019-06-16T22:31:54Z 2003-01-01T00:00:00Z Principal quasi-ideals of cohomological dimension 1 Novikov, B.V. We prove that a principal quasi-ideal of a noncommutative free semigroup has cohomological dimension 1 if and only if it is free. 2003-01-01T00:00:00Z Uniform ball structures Protasov, I.V. http://dspace.nbuv.gov.ua:80/handle/123456789/155282 2019-06-16T22:30:36Z 2003-01-01T00:00:00Z Uniform ball structures Protasov, I.V. A ball structure is a triple B = (X, P, B), where X, P are nonempty sets and, for all 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 introduce the class of uniform ball structures as an asymptotic counterpart of the class of uniform topological spaces. We show that every uniform ball structure can be approximated by metrizable ball structures. We also define two types of ball structures closed to being metrizable, and describe the extremal elements in the classes of ball structures with fixed support X. 2003-01-01T00:00:00Z Almost all derivative quivers of artinian biserial rings contain chains Avdeeva, T. Ganyushkin, O. http://dspace.nbuv.gov.ua:80/handle/123456789/155281 2019-06-16T22:31:35Z 2003-01-01T00:00:00Z Almost all derivative quivers of artinian biserial rings contain chains Avdeeva, T.; Ganyushkin, O. A lower estimate for the number Mn of all labelled quivers with n–vertex parts of Artinian biserial rings is given and the asymptotic of the relation Mn/Bn, where Bn denotes the number of those quivers all connected components of which are cycles, is studied. 2003-01-01T00:00:00Z