It has long been known that every quasi-homogeneous normal complex surface singularity with Q–homology sphere link has universal abelian cover a Brieskorn complete intersection singularity. We describe a broad generalization: First, one has a class of complete intersection normal complex surface singularities called “splice type singularities,” which generalize Brieskorn complete intersections....

We study the properties of rings satisfying Auslander-type conditions. If an artin algebra Λ satisfies the Auslander condition (that is, Λ is an ∞-Gorenstein artin algebra), then we construct two kinds of subcategories which form functorially finite cotorsion theories. Noetherian rings satisfying ‘Auslander-type conditions’ on self-injective resolutions can be regarded as certain non-commutativ...

Let Λ be an Auslander’s 1-Gorenstein Artinian algebra with global dimension two. If Λ admits a trivial maximal 1-orthogonal subcategory of modΛ, then for any indecomposable module M ∈ modΛ, we have that the projective dimension of M is equal to one if and only if so is its injective dimension and that M is injective if the projective dimension of M is equal to two. In this case, we further get ...

Let R be a local Cohen-Macaulay ring with canonical module ωR. We investigate the following question of Huneke: If the sequence of Betti numbers {β i (ωR)} has polynomial growth, must R be Gorenstein? This question is well-understood when R has minimal multiplicity. We investigate this question for a more general class of rings which we say are homologically of minimal multiplicity. We provide ...

We present in this work a generalization of the solution of Gorenstein and Yang to the inconsistency problem of thermodynamics for systems of quasi-particles whose masses depend on both the temperature and the chemical potential. We work out several solutions for an interacting system of quarks and gluons and show that there is only one type of solution that reproduce both perturbative and latt...

We present in this work a generalization of the solution of Gorenstein and Yang for a consistent thermodynamics for systems with a temperature dependent Hamiltonian. We show that there is a large class of solutions, work out three particular ones, and discuss their physical relevance. We apply the particular solutions for an ideal gas of quasi-gluons, and compare the calculation to lattice and ...

Let R be a commutative Noetherian local ring. This paper deals with the problem asking whether R is Gorenstein if the nth syzygy module of the residue class field of R has a non-trivial direct summand of finite Gdimension for some n. It is proved that if n is at most two then it is true, and moreover, the structure of the ring R is determined essentially uniquely.

In this paper, we consider a finite, torsion-free module E over Gorenstein local ring. We provide sufficient conditions for to be of linear type and the Rees algebra R ( ) Cohen-Macaulay. Our results are obtained by constructing generic Bourbaki ideal I exploiting properties residual intersections .

let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $r$.  in this paper we  study the relationship between an$r$-module $m_r$ and the  general polynomial module  $m[x]$ over theskew polynomial ring $r[x;alpha,delta]$. we introduce the notionsof skew-armendariz modules and skew quasi-armendariz modules whichare generalizations of $alpha$-armendariz modules and extend thecla...