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  • Shirikov, Evgenij N. (ДЗ "Луганський національний університет імені Тараса Шевченка, 2005)
    The paper is devoted to classification of two-generated graded algebras. We show that under some general assumptions there exist two classes of these algebras, namely quantum polynomials and Jordanian plane. We study prime ...
  • Koppitz, J¨org; Shtrakov, Slavcho (ДЗ "Луганський національний університет імені Тараса Шевченка, 2005)
    The extensions of hypersubstitutions are mappings on the set of all terms. In the present paper we characterize all hypersubstitutions which provide bijections on the set of all terms. The set of all such hypersubstitutions ...
  • Kanduru Venkata Krishna; Niladri Chatterjee (ДЗ "Луганський національний університет імені Тараса Шевченка, 2005)
    In this work first we study the properties of nearsemirings to introduce an -radical. Then we observe the role of near-semirings in generalized linear sequential machines, and we test the minimality through the radical.
  • Skiba, Alexander N. (ДЗ "Луганський національний університет імені Тараса Шевченка, 2005)
    Let G be a finite group. We fix in every noncyclic Sylow subgroup P of G some its subgroup D satisfying 1 <|D| < |P| and study the structure of G under assumption that all subgroups H of P with |H| = |D| are c-normal in G.
  • Gutik, Oleg V.; Pavlyk, Kateryna P. (ДЗ "Луганський національний університет імені Тараса Шевченка, 2005)
    We prove that the semigroup of matrix units is stable. Compact, countably compact and pseudocompact topologies on the infinite semigroup of matrix units B such that (B , ) is a semitopological (inverse) semigroup are ...
  • Legchekova, Helena V. (ДЗ "Луганський національний університет імені Тараса Шевченка, 2005)
    Let A, B be subgroups of a group G and ∅ 6= X ⊆ G. A subgroup A is said to be X-permutable with B if for some x ∈ X we have ABx = BxA. We obtain some new criterions for supersolubility of a finite group G = AB, where A ...
  • Zekoviс, Biljana (ДЗ "Луганський національний університет імені Тараса Шевченка, 2005)
    In this paper we introduce the notion of a ternary Hopf algebra and prove that it can be embedded into a universal enveloping Hopf algebra.
  • Protasova, K. D. (ДЗ "Луганський національний університет імені Тараса Шевченка, 2005)
    A finite connected graph G is called square-Hamiltonian if G2 is Hamiltonian. We prove that any join of the family of Hamiltonian graphs by tree is square-Hamiltonian. Applying this statement we show that the line graph ...

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