http://dspace.nbuv.gov.ua:80/handle/123456789/150368 2026-04-20T14:27:25Z http://dspace.nbuv.gov.ua:80/handle/123456789/154852 Norm Kloosterman sums over Z[i] Savastru, O.; Varbanets, S. n-dimensional norm Kloosterman sums over the ring of the Gaussian numbers investigate. Nontrivial estimates of these sums were obtained. 2011-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154850 Partitions of groups into thin subsets Protasov, I. Let G be an infinite group with the identity e, κ be an infinite cardinal ≤|G|. A subset A⊂G is called κ-thin if |gA∩A|≤κ for every g∈G∖{e}. We calculate the minimal cardinal μ(G,κ) such that G can be partitioned in μ(G,κ) κ-thin subsets. In particular, we show that the statement μ(R,ℵ₀)=ℵ₀ is equivalent to the Continuum Hypothesis. 2011-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154840 On partial Galois Azumaya extensions Paques, A.; Freitas, D. Let α be a globalizable partial action of a finite group G over a unital ring R, A=R⋆αG the corresponding partial skew group ring, Rα the subring of the α-invariant elements of R and α⋆ the partial inner action of G (induced by α) on the centralizer CA(R) of R in A. In this paper we present equivalent conditions to characterize R as an α-partial Galois Azumaya extension of Rα and CA(R) as an α⋆-partial Galois extension of the center C(A) of A. In particular, we extend to the setting of partial group actions similar results due to R. Alfaro and G. Szeto [1,2,3]. 2011-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/154801 Partial actions and automata Dokuchaev, M.; Novikov, B.; Zholtkevych, G. We use the notion of a partial action of a monoid to introduce a generalization of automata, which we call ``a preautomaton''. We study properties of preautomata and of languages recognized by preautomata. 2011-01-01T00:00:00Z