Selforthogonal modules with finite injective dimension

The category consisting of finitely generated modules which are left orthogonal with a cotilting bimodule is shown to be functorially finite. The notion of left orthogonal dimension is introduced, and then a necessary and sufficient condition of selforthogonal modules having finite injective dimension and a characterization of cotilting modules are given.     

有限内射维数的余倾斜余模(英文)

本文中,受C.Nastasescu etc.和Y.Miyashita思想的影响,定义了余代数的余倾斜余模,研究得出有限内射维数的余倾斜余模的一些结论.     

A generalization of the Auslander transpose and the generalized Gorenstein dimension

Let R be a left and right Noetherian ring and C a semidualizing R-bimodule. We introduce a transpose Tr _c M of an R-module M with respect to C which unifies the Auslander transpose and Huang’s transpose, see Z.Y.Huang, On a generalization of the Auslander-Bridger transpose, Comm. Algebra 27 (1999), 5791–5812, in the two-sided Noetherian setting, and use Tr _c M to develop further the generalized Gorenstein dimension with respect to C. Especially, we generalize the Auslander-Bridger formula to the generalized Gorenstein dimension case. These results extend the corresponding ones on the Gorenstein dimension obtained by Auslander in M. Auslander, M. Bridger, Stable Module Theory, Mem. Amer. Math. Soc. vol. 94, Amer. Math. Soc., Providence, RI, 1969.     

On the Existence of Relative Injective Covers

Let be a hereditary torsion theory for the category -mod of unital left -modules over an associative ring with an identity element. The purpose of this note is to prove that if the associated Gabriel filter consists of finitely presented left ideals, then every module has a -injective cover and if contains a cofinal subset of finitely presented left ideals, then every module has a -torsionfree -injective cover. The methods used working with pure submodules contained in ``large" submodules also allow to unify the proofs of some previously known results.     

On the Existence of Certain Modules of Finite Gorenstein Homological Dimensions

Let (R, 𝔪) be a commutative Noetherian local ring. It is known that R is Cohen–Macaulay if there exists either a nonzero finitely generated R-module of finite injective dimension or a nonzero Cohen–Macaulay R-module of finite projective dimension. In this article, we investigate the Gorenstein analogues of these facts.     

On the Constant Metric Dimension of Generalized Petersen Graphs P（n, 4）

In this paper,we consider the family of generalized Petersen graphs P(n,4).We prove that the metric dimension of P(n,4) is 3 when n ≡ 0(mod 4),and is 4 when n = 4k + 3(k is even).For n ≡ 1,2(mod 4) and n = 4k + 3(k is odd),we prove that the metric dimension of P(n,4) is bounded above by 4.This shows that each graph of the family of generalized Petersen graphs P(n,4)has constant metric dimension.     

Gorenstein Injective and Gorenstein Flat Resolution of Modules Over Gorenstein Rings

Abstract

Let R be a commutative Noetherian ring. There are several characterizations of Gorenstein rings in terms of classical homological dimensions of their modules. In this paper, we use Gorenstein dimensions (Gorenstein injective and Gorenstein flat dimension) to describe Gorenstein rings. Moreover a characterization of Gorenstein injective (resp. Gorenstein flat) modules over Gorenstein rings is given in terms of their Gorenstein flat (resp. Gorenstein injective) resolutions.     

On the global balanced-projective dimension of valuation domains

Assuming the General Continuum Hypothesis, the global balanced-projective dimension of a valuation domain is determined. We show that it is always equal to the supremum of the projective dimensions of torsion-free modules.     

FI性质的传递

一个环R称为左(右)FI环，如果它的每一个平坦左(右)R模是内射的，R称为FI环是指它既是左且右的FI环．本讨论了当R是FI环时，其多项式环R[t]，矩阵环MN(R)以及分式不S^-1R也是FI环的充分与必要条件．     

On the generalization of a retrocirculant

We study the properties of matrices of the form P(σ)A where σ is induced by an automorphism of an abelian group G and A is a group matrix. P(σ)A is a generalization of a retrocirculant. We also determine the eigenvalues of P(σ)A.     

关于内射维数有限的cotilting余模

令K是域,设C是一个K-余代数,T为cotilting左C-余模,通过对cotilting余模的性质和理论的研究,得到关于cotilting余模的一些有意义的结果.     

On a generalization of the logistic distribution

Summary Expressions for the moment generating functions, cumulants and coefficients of kurtosis of a generalization of the logistic distribution are derived and used to show that any symmetric version of this distribution can be closely and simply approximated by a Studentt distribution. Related approximation of the distribution of the logistic sample median is discussed.     

On a generalization of the Evans Conjecture

The Evans Conjecture states that a partial Latin square of order n with at most n-1 entries can be completed. In this paper we generalize the Evans Conjecture by showing that a partial r-multi Latin square of order n with at most n-1 entries can be completed. Using this generalization, we confirm a case of a conjecture of Häggkvist.     

On a generalization of the bessel inequality

Translated from Matematicheskie Zametki, Vol. 51, No. 5, pp. 149–150, May, 1992.     

On a generalization of the Keldysh theorem

The Keldysh theorem for an elliptic equation with characteristic parabolic degeneration is generalized for the case of an elliptic equation of the second-order canonical form with order and type degeneration. The criteria under which the Dirichlet or Keldysh problems are correct are given in a one-sided neighborhood of the degeneration segment, enabling one to write the criteria in a single form. Moreover, some cases are pointed out in which it is even nessesary to give a criterion in the neighborhood because it is impossible to establish it on the segment of degeneracy of the equation.     

On a generalization of the Lambert series

Summary The asymptotic behavior in the neighborhood of x=1 is determined of the function Σ(n+θ)^γ xα(n+θ)β(0<x<1). In the special case α=ϑ=1, β=−1, γ=0 a sharp numerical upper bound is given for the absolute value of the error term. This problem is used to expose a general principle in asympototics. To Enrico Bompiani on his scientific Jubilee     

On a generalization of the Kalman-Yakubovic lemma

In this paper we generalize the Kalman-Yakubovic lemma to infinite dimensions—or, more precisely, to semigroups of operators over a Hilbert space. The proof differs substantially from the finite-dimensional version and is based on the Paley-Wiener-Helson-Lowdenslager factorization theorem.