1. Introduction. We present two closely related results connecting homological dimension theory and the ideal theory of noetherian rings. The first, Proposition 4.1, asserts that the only ideals of finite homological dimension in a local ring whose associated prime ideals all have grade one are of the form aR:bR. The second, Proposition 4.3, asserts that if R is a noetherian integral domain, th...

It was proved by Avramov and Buchweitz that if A is a commutative local complete intersection ring with finitely generated modules M and N , then the Ext groups between M and N vanish from some step if and only if the Ext groups between N and M vanish from some step. This paper shows that the same is true under the weaker conditions that A is Gorenstein and that M and N have finite complete int...

It is a conjecture due to M. E. Rossi that the Hilbert function of a one-dimensional Gorenstein local ring is non-decreasing. In this article, we show that the Hilbert function is non-decreasing for local Gorenstein rings with embedding dimension four associated to monomial curves, under some arithmetic assumptions on the generators of their defining ideals in the noncomplete intersection case....

Abstract. The conjecture on roots of Ehrhart polynomials, stated by Matsui et al. [15, Conjecture 4.10], says that all roots α of the Ehrhart polynomial of a Gorenstein Fano polytope of dimension d satisfy − d 2 ≤ Re(α) ≤ d 2 − 1. In this paper, we observe the behaviors of roots of SSNN polynomials which are a wider class of the polynomials containing all the Ehrhart polynomials of Gorenstein F...

We introduce and investigate the notion of GC -projective modules over (possibly non-noetherian) commutative rings, where C is a semidualizing module. This extends Holm and Jørgensen’s notion of C-Gorenstein projective modules to the non-noetherian setting and generalizes projective and Gorenstein projective modules within this setting. We then study the resulting modules of finite GC-projectiv...

We give an exposition and generalization of Orlov’s theorem on graded Gorenstein rings. We show the theorem holds for non-negatively graded rings which are Gorenstein in an appropriate sense and whose degree zero component is an arbitrary non-commutative right noetherian ring of finite global dimension. A short treatment of some foundations for local cohomology and Grothendieck duality at this ...

We give a convolution formula for cd-index coefficients. The convolution formula, together with the proof by Davis and Okun of the CharneyDavis Conjecture in dimension 3, imply that certain cd-coefficients are nonnegative for all Gorenstein* posets. Additional coefficients are shown to be non-negative by interpreting them in terms of the top homology of certain Cohen-Macaulay complexes. In part...

In this article we investigate the relations between Gorenstein projective dimensions of [Formula: see text]-modules and their socles for text]-minimal Auslander–Gorenstein algebras text]. First give a description projective-injective in terms socles. Then prove that text]-module text] has dimension at most if only its socle is cogenerated by text]-module. Furthermore, show can be characterised...

Tate local cohomology and Gorenstein theory, which are important generalizations of the classical cohomology, has been investigated. It found that they have such vanishing properties long exact sequences. However, for homology, what about duality? In this paper we concerned with homology homology. first part generalize as study properties, artinianness some sequence modules. We find an artiania...

Let R be a ring with identity and C(R) denote the category of complexes of R-modules. In this paper we study the homotopy categories arising from projective (resp. injective) complexes as well as Gorenstein projective (resp. Gorenstein injective) modules. We show that the homotopy category of projective complexes over R, denoted K(Prj C(R)), is always well generated and is compactly generated p...