Перегляд за автором "Dokuchaev, M.A."

Сортувати за: Порядок: Результатів:

  • Exponent matrices and Frobenius rings 
    Dokuchaev, M.A.; Kasyanuk, M.V.; Khibina, M.A.; Kirichenko, V.V. (Algebra and Discrete Mathematics, 2014)
    We give a survey of results connecting the exponent matrices with Frobenius rings. In particular, we prove that for any parmutation σ ∈ Sn there exists a countable set of indecomposable Frobenius semidistributive rings Am ...
  • Gorenstein Latin squares 
    Dokuchaev, M.A.; Kirichenko, V.V.; Novikov, B.V.; Plakhotnyk, M.V. (Algebra and Discrete Mathematics, 2008)
    We introduce the notion of a Gorenstein Latin square and consider loops and quasigroups related to them. We study some properties of normalized Gorenstein Latin squares and describe all of them with order n≤8.
  • Gorenstein matrices 
    Dokuchaev, M.A.; Kirichenko, V.V.; Zelensky, A.V.; Zhuravlev, V.N. (Algebra and Discrete Mathematics, 2005)
    Let A = (aij ) be an integral matrix. We say that A is (0, 1, 2)-matrix if aij ∈ {0, 1, 2}. There exists the Gorenstein (0, 1, 2)-matrix for any permutation σ on the set {1, . . . , n} without fixed elements. For every ...
  • Quasi-Frobenius Rings and Nakayama Permutations of Semiperfect Rings 
    Dokuchaev, M.A.; Kirichenko, V.V. (Український математичний журнал, 2002)
    We say that A is a ring with duality for simple modules, or simply a DSM-ring, if, for every simple right (left) A-module U, the dual module U* is a simple left (right) A-module. We prove that a semiperfect ring is a ...
  • Rings with finite decomposition of identity 
    Dokuchaev, M.A.; Gubareni, N.M.; Kirichenko, V.V. (Український математичний журнал, 2011)
    A criterion for semiprime rings with finite decomposition of identity to be prime is given. We also give a short survey on some finiteness conditions related to the decomposition of identity. We consider the notion of a ...
  • Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. I 
    Chernousova, Zh.T.; Dokuchaev, M.A.; Khibina, M.A.; Kirichenko, V.V.; Miroshnichenko, S.G.; Zhuravlev, V.N. (Algebra and Discrete Mathematics, 2002)
    We prove that the quiver of tiled order over a discrete valuation ring is strongly connected and simply laced. With such quiver we associate a finite ergodic Markov chain. We introduce the notion of the index in A of a ...
  • Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II 
    Chernousova, Zh.T.; Dokuchaev, M.A.; Khibina, M.A.; Kirichenko, V.V.; Miroshnichenko, S.G.; Zhuravlev, V.N. (Algebra and Discrete Mathematics, 2003)
    The main concept of this part of the paper is that of a reduced exponent matrix and its quiver, which is strongly connected and simply laced. We give the description of quivers of reduced Gorenstein exponent matrices ...