http://dspace.nbuv.gov.ua:80/handle/123456789/188470 2026-04-22T14:32:25Z http://dspace.nbuv.gov.ua:80/handle/123456789/188522 Poisson brackets on some skew PBW extensions Zambrano, B.A. In [1] the author gives a description of Poisson brackets on some algebras of quantum polynomials Oq, which is called the general algebra of quantum polynomials. The main of this paper is to present a generalization of [1] through a description of Poisson brackets on some skew PBW extensions of a ring A by the extensions Oʳ,ⁿq,δ , which are generalization of Oq, and show some examples of skew PBW extension where we can apply this description. 2020-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188521 Elementary reduction of matrices over rings of almost stable range 1 Zabavsky, B.; Romaniv, A.; Kysil, T. In this paper we consider elementary reduction of matrices over rings of almost stable range 1. 2020-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188520 Norm of Gaussian integers in arithmetical progressions and narrow sectors Varbanets, S.; Vorobyov, Y. We proved the equidistribution of the Gaussian integer numbers in narrow sectors of the circle of radius x¹/² , x → ∞, with the norms belonging to arithmetic progression N(α) ≡ ℓ (mod q) with the common difference of an arithmetic progression q, q ≪ x²/³⁻ᵋ. 2020-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/188519 On a common generalization of symmetric rings and quasi duo rings Subedi, T.; Roy, D. Let J(R) denote the Jacobson radical of a ring R. We call a ring R as J-symmetric if for any a, b, c ∈ R, abc = 0 implies bac ∈ J(R). It turns out that J-symmetric rings are a common generalization of left (right) quasi-duo rings and generalized weakly symmetric rings. Various properties of these rings are established and some results on exchange rings and the regularity of left SF-rings are generalized. 2020-01-01T00:00:00Z