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  • On the anticommutativity in Leibniz algebras 
    Kurdachenko, L.; Semko, N.; Subbotin, I. (2018)
    Lie algebras are exactly the anticommutative Leibniz algebras. In this article, we conduct a brief analysis of the approach to Leibniz algebras which based on the concept of the anti-center (Lie-center) and antinilpotency ...
  • On the difference between the spectral radius and the maximum degree of graphs∗ 
    Oboudi, M.R. (ДЗ "ЛНУ імені Тараса Шевченка", 2017)
    Let G be a graph with the eigenvalues λ1(G) >· · · > λn(G). The largest eigenvalue of G, λ1(G), is called the spectral radius of G. Let β(G) = ∆(G) − λ1(G), where ∆(G) is the maximum degree of vertices of G. It is known ...
  • On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs 
    Simson, D. (ДЗ "ЛНУ імені Тараса Шевченка", 2019)
    Magic rectangles are a classical generalization of the well-known magic squares, and they are related to graphs. A graph G is called degree-magic if there exists a labelling of the edges by integers 1, 2, . . . , |E(G)| ...
  • On the finite state automorphism group of a rooted tree 
    Lavrenyuk, Yaroslav (Луганский национальный университет им. Т. Шевченко, 2002-09-23)
  • On the Fitting ideals of a multiplication module 
    Hadjirezaei, S.; Karimzadeh, S. (ДЗ "ЛНУ імені Тараса Шевченка", 2019)
    In this paper, we characterize all finitely gene- rated multiplication R-modules whose the first nonzero Fitting ideal of them is contained in only finitely many maximal ideals. Also, we prove that a finitely generated ...
  • On the genus of the annihilator graph of a commutative ring 
    Chelvam, T. T.; Selvakumar, K. (2017)
    Let R be a commutative ring and Z(R) ∗ be its set of non-zero zero-divisors. The annihilator graph of a commu- tative ring R is the simple undirected graph AG(R) with vertices Z(R) ∗ , and two distinct vertices ...
  • On the group of extensions for the bicrossed product construction for a locally compact group 
    Chapovsky, Yu. A.; Kalyuzhnyi, A. A.; Podkolzin, G. B. (Луганский национальный университет им. Т. Шевченко, 2004)
    For the cocycle bicrossed product construction applied to a locally compact group and its two subgroups, we give a simple description of the group of the corresponding extensions in terms of the second cohomology group ...
  • On the inclusion ideal graph of a poset 
    Jahanbakhsh, N .; Nikandish, R.; Nikmehr, M. J . (2019)
    Let (P, 6) be an atomic partially ordered set (poset, briefly) with a minimum element 0 and I(P) the set of nontrivial ideals of P. The inclusion ideal graph of P, denoted by Ω(P), is an undirected and simple graph with ...
  • On the lattice of cyclic codes over finite chain rings 
    Fotue -Tabue, A .; Mouaha, C. (2019)
    In this paper, R is a finite chain ring of invariants (q, s), and l is a positive integer fulfilling gcd(l, q) = 1. In the language of q-cyclotomic cosets modulo l, the cyclic codes over R of length l are uniquely decomposed ...
  • ON THE LEAST SEMIGROUP CONGRUENCES ON DIMONOIDS 
    Zhuchok, Y. V. (2014)
  • On the mean square of the Epstein zeta-function 
    Savastru, O. V.; Varbanets, P. D. (Луганский национальный университет им. Т. Шевченко, 2005)
    We consider the second power moment of the Epstein zeta-function and construct the asymptotic formula in special case, when '0(u, v) = u2 + Av2, A > 0, A 1, 2(mod 4) and '0(u, v) belongs to the one-class kind G0 of the ...
  • On the number of topologies on a finite set 
    Kizmaz, M. Y. (2019)
    We denote the number of distinct topologies which can be defined on a set X with n elements by T(n). Similarly, T0(n) denotes the number of distinct T0 topologies on the set X. In the present paper, we prove that for ...
  • On the representation of a number as a sum of the k-th powers in an arithmetic progression 
    Prosyanyuk, N.S. (Луганский национальный университет им. Т. Шевченко, 2003-02-27)
  • On the representation type of Jordan basic algebras 
    Kashuba, I.; Ovsienko, S.; Shestakov, I. (ДЗ "ЛНУ імені Тараса Шевченка", 2017)
    A finite dimensional Jordan algebra J over a field k is called basic if the quotient algebra J/ Rad J is isomorphic to a direct sum of copies of k. We describe all basic Jordan algebras J with (Rad J) 2 = 0 of finite and ...
  • On the saturations of submodules 
    Paudel, L.; Tchamna, S. (2018)
    Let R ⊆ S be a ring extension, and let A be an R-submodule of S. The saturation of A (in S) by τ is set A[τ] = {x ∈ S : tx ∈ A for some t ∈ τ}, where τ is a multiplicative subset of R. We study properties of saturations ...
  • On the separability of the restriction functor 
    Theohari-Apostolidi, Th.; Vavatsoulas, H. (Луганский национальный университет им. Т. Шевченко, 2003-06-26)
  • On the spectrum and spectrum multiplicities of a sum of orthogonal projections 
    Kyrychenko, A. A.; Samoˇılenko, Yu. S. (Луганский национальный университет им. Т. Шевченко, 2004)
  • On the Tits alternative for some generalized triangle groups 
    Beniash-Kryvets, Valery; Barkovich, Oxana (Луганский национальный университет им. Т. Шевченко, 2004-02-24)
  • On the zero forcing number of graphs and their splitting graphs 
    Chacko, B.; Dominic, C.; Premodkumar, K. P. (ДЗ "ЛНУ імені Тараса Шевченка", 2019)
    In [10], the notion of the splitting graph of a graph was introduced. In this paper we compute the zero forcing number of the splitting graph of a graph and also obtain some bounds besides finding the exact value of ...
  • On unicyclic graphs of metric dimension 2 
    Dudenko, M.; Oliynyk, B. (2017)
    A metric basis S of a graph G is the subset of vertices of minimum cardinality such that all other vertices are uniquely determined by their distances to the vertices in S. The metric dimension of a graph G is the ...