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Browsing Algebra and Discrete Mathematics. - № 1 (23). - 2017 by Title

Browsing Algebra and Discrete Mathematics. - № 1 (23). - 2017 by Title

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  • A criterion of elementary divisor domain for distributive domains 
    Bokhonko, V.; Zabavsky, B. (ДЗ "ЛНУ імені Тараса Шевченка", 2017)
    In this paper we introduce the notion of the neat range one for Bezout duo-domains. We show that a distributive Bezout domain is an elementary divisor domain if and only if it is a duo-domain of neat range one.
  • A new way to construct 1-singular Gelfand-Tsetlin modules 
    Zadunaisky, P. (ДЗ "ЛНУ імені Тараса Шевченка", 2017)
    We present a simplified way to construct the Gelfand-Tsetlin modules over gl(n, C) related to a 1-singular GT- tableau defined in [6]. We begin by reframing the classical construc- tion of generic Gelfand-Tsetlin ...
  • Dg algebras with enough idempotents, their dg modules and their derived categories 
    M., Saorín (ДЗ "ЛНУ імені Тараса Шевченка", 2017)
    We develop the theory dg algebras with enough idempotents and their dg modules and show their equivalence with that of small dg categories and their dg modules. We introduce the concept of dg adjunction and show that ...
  • Equivalence of Carter diagrams 
    Stekolshchik, R. (ДЗ "ЛНУ імені Тараса Шевченка", 2017)
    We introduce the equivalence relation ρ on the set of Carter diagrams and construct an explicit transformation of any Carter diagram containing l-cycles with l > 4 to an equivalent Carter diagram containing only 4-cycles. ...
  • Galois orders of symmetric differential operators 
    Futorny, V.; Schwarz, J. (ДЗ "ЛНУ імені Тараса Шевченка", 2017)
    In this survey we discuss the theory of Galois rings and orders developed in by Sergey Ovsienko and the first author. This concept allows to unify the representation theories of Generalized Weyl Algebras and of the ...
  • On representations of the group of order two over local factorial rings in the weakly modular case 
    Bondarenko, V.M.; Stoika, M.V. (ДЗ "ЛНУ імені Тараса Шевченка", 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 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 ...
  • Representations of nodal algebras of type E 
    Drozd, Y.; Golovashchuk, N.; Zembyk, V. (2017)
    We define representation types of nodal algebras of type E.

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