Перегляд за автором "Bondarenko, V.M."

Сортувати за: Порядок: Результатів:

  • Indecomposable and irreducible t-monomial matrices over commutative rings 
    Bondarenko, V.M.; Bortos, M.; Dinis, R.; Tylyshchak, A. (Algebra and Discrete Mathematics, 2016)
    We introduce the notion of the defining sequence of a permutation indecomposable monomial matrix over a commutative ring and obtain necessary conditions for such matrices to be indecomposable or irreducible in terms ...
  • Minimax isomorphism algorithm and primitive posets 
    Bondarenko, V.M. (Algebra and Discrete Mathematics, 2011)
    The notion of minimax equivalence of posets, and a close notion of minimax isomorphism, introduced by the author are widely used in the study of quadratic Tits forms (in particular, for the description of P-critical ...
  • Minimax sums of posets and the quadratic Tits form 
    Bondarenko, V.M.; Polishchuk, A.M. (Algebra and Discrete Mathematics, 2004)
    In this paper we study the structure of infinite posets with positive Tits form. In particular, there arise posets of specific form which we call minimax sums of posets.
  • On a deformation diameter of Dynkin diagrams 
    Bondarenko, V.M.; Bondarenko, V.V.; Lisykevych, V.A.; Pereguda, Y.M. (Algebra and Discrete Mathematics, 2015)
    We introduce the notion of a deformation distance and calculate the diameter of Dynkin diagrams respect to this distance.
  • On characteristic properties of semigroups 
    Bondarenko, V.M.; Zaciha, Ya.V. (Algebra and Discrete Mathematics, 2015)
    Let K be a class of semigroups and P be a set of general properties of semigroups. We call a subset Q of P characteristic for a semigroup S ∈ K if, up to isomorphism and antiisomorphism, S is the only semigroup in K, which ...
  • On characteristic properties of semigroups 
    Bondarenko, V.M.; Zaciha, Y.V. (Algebra and Discrete Mathematics, 2015)
    Let K be a class of semigroups and P be a set of general properties of semigroups. We call a subset Q of P cha\-racteristic for a semigroup S∈ K if, up to isomorphism and anti-isomorphism, S is the only semigroup in ...
  • On classification of pairs of potent linear operators with the simplest annihilation condition 
    Bondarenko, V.M.; Tertychna, O.M.; Zubaruk, O.V. (Algebra and Discrete Mathematics, 2016)
    We study the problem of classifying the pairs of linear operators A,B (acting on the same vector space), when the both operators are potent and AB=0. We describe the finite, tame and wild cases and classify the indecomposable ...
  • On classifying the non-Tits P-critical posets 
    Bondarenko, V.M.; Styopochkina, M.V. (Algebra and Discrete Mathematics, 2021)
    In 2005, the authors described all introduced by them P-critical posets (minimal finite posets with the quadratic Tits form not being positive); up to isomorphism, their number is 132 (75 if duality is considered). Later ...
  • On connections between representations of semigroups S(I,J) and representations of quivers 
    Bondarenko, V.M. (2009)
    In this paper we study connections between representations of one natural class of semigroups and representations of quivers.
  • On dispersing representations of quivers and their connection with representations of bundles of semichains 
    Bondarenko, V.M. (Algebra and Discrete Mathematics, 2002)
    In the paper we discuss the notion of “dispersing representation of a quiver” and give, in a natural special case, a criterion for the problem of classifying such representations to be tame. In proving the criterion we ...
  • On finite posets of injinj-finite type and their Tits forms 
    Bondarenko, V.M.; Styopochkina, M.V. (Algebra and Discrete Mathematics, 2006)
    We prove one theorem on connection between inj-finiteness of a finite poset and positive definiteness of its Tits form.
  • On hereditary reducibility of 2-monomial matrices over commutative rings 
    Bondarenko, V.M.; Gildea, J.; Tylyshchak, A.A.; Yurchenko, N.V. (Algebra and Discrete Mathematics, 2019)
    In this paper we introduce the notion of hereditary reducibility for some matrices and indicate one general condition of the introduced reducibility.
  • On P-numbers of quadratic forms 
    Bondarenko, V.M.; Pereguda, Yu.M. (2009)
    In this paper we introduce P-numbers of quadratic forms over R and study their properties.
  • On posets of width two with positive Tits form 
    Bondarenko, V.M.; Styopochkina, M.V. (Algebra and Discrete Mathematics, 2005)
    We give a complete description of the finite posets of width two with the Tits form to be positive. This problem arises in studying the categories of representations of posets of finite type.
  • On representations of the group of order two over local factorial rings in the weakly modular case 
    Bondarenko, V.M.; Stoika, M. (Algebra and Discrete Mathematics, 2017)
    We study representations of the group of order 2 over local factorial rings of characteristic not 2 with residue field of characteristic 2. The main results are related to a sufficient condition of wildness of groups.
  • On representations of the semigroups S(I,J) with acyclic quiver 
    Bondarenko, V.M.; Tertychna, O.M. (2009)
    In this paper we study representations of semigroups (over a field k) generated by idempotents with partial null multiplication in the case when the corresponding quiver has not oriented cycles.
  • On representation type of a pair of posets with involution 
    Bondarenko, V.M. (Algebra and Discrete Mathematics, 2005)
    In this paper we consider the problem on classifying the representations of a pair of posets with involution. We prove that if one of these is a chain of length at least 4 with trivial involution and the other is with ...
  • On tame semigroups generated by idempotents with partial null multiplication 
    Bondarenko, V.M.; Tertychna, O.M. (Algebra and Discrete Mathematics, 2008)
    Let I be a finite set without 0 and J a subset in I×I without diagonal elements (i,i). We define S(I,J) to be the semigroup with generators ei, where i∈I∪0, and the following relations: e0=0; e2i=ei for any i∈I; eiej=0 ...
  • On the equivalence of matrices over commutative rings modulo ideals 
    Bondarenko, V.M.; Tylyshchak, A.A.; Stoika, M.V. (Algebra and Discrete Mathematics, 2014)
    We study connections between wildness of the problem of classifying the matrices over an integral domain up to equivalence modulo an ideal and properties of the set of prime elements of the domain.
  • On types of local deformations of quadratic forms 
    Bondarenko, V.M. (Algebra and Discrete Mathematics, 2014)
    We consider some aspects of the theory of quadratic forms concerning their local deformations.