相关论文: Contracting Endomorphisms and Gorenstein Modules
We prove several characterizations of Gorenstein rings in terms of vanishings of derived functors of certain modules or complexes whose scalars are restricted via contracting endomorphisms. These results can be viewed as analogues of…
In this paper we study homological dimensions of finitely generated modules over commutative Noetherian local rings, called reducing homological dimensions. We obtain new characterizations of Gorenstein and complete intersection local rings…
The Gorenstein property in local algebra admits several characterizations via its module category. The goal of this paper is to collect and generalize such characterizations to the relative setting, i.e., to Gorenstein morphisms as defined…
We define, via Gorenstein homomorphisms, a class of local rings over which there exist non-trivial totally reflexive modules. We also provide a general construction of such rings, which indicates their abundance.
In this paper, some new characterizations on Gorenstein projective, injective and flat modules over commutative noetherian local ring are given.
Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical…
We develop a theory of G-dimension for modules over local homomorphisms which encompasses the classical theory of G-dimension for finite modules over local rings. As an application, we prove that a local ring R of characteristic p is…
We describe the endomorphism rings of maximal rigid objects in the cluster categories of tubes. Moreover, we show that they are gentle and have Gorenstein dimension 1. We analyse their representation theory and prove that they are of finite…
We characterize the Gorensteinness of endomorphism rings of a fractional ideal on a curve singularity by stability of the ideal and a condition on its value semigroup ideal. Moreover, the Gorenstein algebroid curves with only Gorenstein…
New homotopy invariant finiteness conditions on modules over commutative rings are introduced, and their properties are studied systematically. A number of finiteness results for classical homological invariants like flat dimension,…
We study homological properties of test modules that are, in principle, modules that detect finite homological dimensions. The main outcome of our results is a generalization of a classical theorem of Auslander and Bridger: we prove that,…
In this paper, we prove that certain contravariant endofunctors of singularity categories characterize Gorenstein rings.
Regularity, complete intersection and Gorenstein properties of a local ring can be characterized by homological conditions on the canonical homomorphism into its residue field (Serre, Avramov, Auslander). It is also known that in positive…
This paper is devoted to present some characterizations for a local ring to be generically Gorenstein and Gorenstein by means of $\delta$-invariant and linkage theory.
We study the construction and properties of modules whose endomorphism rings have a unique two-sided maximal ideal.
Starting from the notion of totally reflexive modules, we survey the theory of Gorenstein homological dimensions for modules over commutative rings. The account includes the theory's connections with relative homological algebra and with…
Let $M$ denote a finitely generated module over a Noetherian ring $R$. For an ideal $I \subset R$ there is a study of the endomorphisms of the local cohomology module $H^g_I(M), g = \operatorname{grade} (I,M),$ and related results. Another…
(Partial) Gorenstein silting modules are introduced and investigated. It is shown that for finite dimensional algebras of finite CM-type, partial Gorenstein silting modules are in bijection with {\tau}_G-rigid modules; Gorenstein silting…
A generalization of Grothendieck's non-vanishing theorem is proved for a module which is finite over a local homomorphism. It is also proved that the Gorenstein injective dimension of such a module, if finite, is bounded below by its Krull…
Let R be a commutative Noetherian local ring. We show that R is Gorenstein if and only if every finitely generated R-module can be embedded in a finitely generated R-module of finite projective dimension. This extends a result of Auslander…