Algebra and Discrete Mathematics, 2020, Vol. 29, № 2http://dspace.nbuv.gov.ua:80/handle/123456789/1884702026-04-22T14:32:33Z2026-04-22T14:32:33ZPoisson brackets on some skew PBW extensionsZambrano, B.A.http://dspace.nbuv.gov.ua:80/handle/123456789/1885222023-03-03T23:27:09Z2020-01-01T00:00:00ZPoisson 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.
2020-01-01T00:00:00ZElementary reduction of matrices over rings of almost stable range 1Zabavsky, B.Romaniv, A.Kysil, T.http://dspace.nbuv.gov.ua:80/handle/123456789/1885212023-03-03T23:27:12Z2020-01-01T00:00:00ZElementary 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.
2020-01-01T00:00:00ZNorm of Gaussian integers in arithmetical progressions and narrow sectorsVarbanets, S.Vorobyov, Y.http://dspace.nbuv.gov.ua:80/handle/123456789/1885202023-03-03T23:27:08Z2020-01-01T00:00:00ZNorm 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.
2020-01-01T00:00:00ZOn a common generalization of symmetric rings and quasi duo ringsSubedi, T.Roy, D.http://dspace.nbuv.gov.ua:80/handle/123456789/1885192023-03-03T23:27:16Z2020-01-01T00:00:00ZOn 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