54 research outputs found

    On semiperfect rings of injective dimension one

    Get PDF
    We give a characterization of right Noetherian semiprimesemiperfect and semidistributive rings with inj. dimAAA 6 1

    Gorenstein Quivers

    Get PDF
    We introduce a notion of Gorenstein quiver associated witha Gorenstein matrix. We study properties of such quivers. In partic-ular, we show that any such quiver is strongly connected and simplylaced. We use Perron-Frobenius theory of non-negative matrices forcharacterization of isomorphic Gorenstein quivers

    Tiled orders over discrete valuation rings, finite Markov chains and partially ordered sets. II

    No full text
    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 whose number s of vertices is at most 7. For 2 ≀ 6 s ≀ 5 we have that all adjacency matrices of such quivers are multiples of doubly stochastic matrices. We prove that for any permutation Οƒ on n letters without fixed elements there exists a reduced Gorenstein tiled order Ξ› with Οƒ(Ξ΅) = Οƒ. We show that for any positive integer k there exists a Gorenstein tiled order Ξ›k with inΞ›k = k. The adjacency matrix of any cyclic Gorenstein order Ξ› is a linear combination of powers of a permutation matrix PΟƒ with non-negative coefficients, where Οƒ = Οƒ(Ξ›). If A is a noetherian prime semiperfect semidistributive ring of a finite global dimension, then Q(A) be a strongly connected simply laced quiver which has no loops

    Gorenstein matrices

    No full text
    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 Οƒ on the set {1, . . . , n} without fixed elements. For every positive integer n there exists the Gorenstein cyclic (0, 1, 2)-matrix An such that inx An = 2. If a Latin square Ln with a first row and first column (0, 1, . . . n βˆ’ 1) is an exponent matrix, then n = 2m and Ln is the Cayley table of a direct product of m copies of the cyclic group of order 2. Conversely, the Cayley table Em of the elementary abelian group Gm = (2)Γ—. . .Γ—(2) of order 2 m is a Latin square and a Gorenstein symmetric matrix with first row (0, 1, . . . , 2 m βˆ’ 1) and Οƒ(Em) = 1 2 3 . . . 2 m βˆ’ 1 2m 2 m 2 m βˆ’ 1 2m βˆ’ 2 . . . 2 1

    Quivers of 3Γ—3 exponent matrices

    No full text
    We show how to use generating exponent matrices to study the quivers of exponent matrices. We also describe the admissible quivers of 3Γ—3 exponent matrices

    Quivers of 3Γ—3-exponent matrices

    Get PDF
    We show how to use generating exponent matrices to study the quivers of exponent matrices. We also describe the admissible quivers of 3Γ—3 exponent matrices

    Projective resolution of irreducible modules over tiled order

    No full text
    We indicate the method for computing the kernels of projective resolution of irreducible module over tiled order. On the base of this method we construct projective resolution of irreducible module and calculate the global dimension of tiled order. The evident view of kernels of projective resolution allows to check easily the regularity of tiled order

    Gorenstein tiled orders

    Full text link

    Tiled orders of width 3

    No full text
    We consider projective cover over tiled order and calculate the kernel of epimorphism from direct sum of submodules of distributive module to their sum
    • …
    corecore