Related papers: Rigid modules and homological dimensions

We introduce Gorenstein silting modules (resp. complexes), and give the relation with the usual silting modules (resp. complexes). We show that Gorenstein silting modules are the module-theoretic counterpart of 2-term Gorenstein silting…

Let $(R,\fm)$ be a local ring and $(-)^{\vee}$ denote the Matlis duality functor. We investigate the relationship between Foxby equivalence and local duality through generalized local cohomology modules. Assume that $R$ possesses a…

We study certain integer valued length functions on triangulated categories and establish a correspondence between such functions and cohomological functors taking values in the category of finite length modules over some ring. The…

The notion of Burch ideals and Burch submodules were introduced (and studied) by Dao-Kobayashi-Takahashi in 2020 and Dey-Kobayashi in 2022 respectively. The aim of this article is to characterize various local rings in terms of homological…

The main focus is the generic freeness of local cohomology modules in a graded setting. The present approach takes place in a quite nonrestrictive setting, by solely assuming that the ground coefficient ring is Noetherian. Under additional…

We define and study a notion of G-dimension for DG-modules over a non-positively graded commutative noetherian DG-ring $A$. Some criteria for the finiteness of the G-dimension of a DG-module are given by applying a DG-version of projective…

In this paper, we extend the well-known Hilbert's syzygy theorem to the Gorenstein homological dimensions of rings. Also, we study the Gorenstein homological dimensions of direct products of rings. Our results generate examples of…

We study criteria for a ring - or more generally, for a small category - to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to…

We investigate finiteness conditions on modules of bounded projective dimension and their connection with generalized notions of coherence. For a ring $R$, we consider the class $\mathsf{FP}_n^{\le d}(R)$ of finitely $n$-presented modules…

Under semi-weak and weak compatibility of bimodules, we establish sufficient and necessary conditions of Gorenstein-projective modules over rings of Morita contexts with one bimodule homomorphism zero. This generalises and extends results…

Let $ R $ be a $ d $-dimensional Cohen-Macaulay (CM) local ring of minimal multiplicity. Set $ S := R/({\bf f}) $, where $ {\bf f} := f_1,\ldots,f_c $ is an $ R $-regular sequence. Suppose $ M $ and $ N $ are maximal CM $ S $-modules. It is…

We show that Iacob-Iyengar's answer to a question of Avromov-Foxby extends from Noetherian to coherent rings. In particular, a coherent ring R is regular if and only if the injective (resp. projective) dimension of each complex X of…

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…

In this note, we extend the quasi-projective dimension of finite (that is, finitely generated) modules to homologically finite complexes, and we investigate some of homological properties of this dimension.

This work builds on earlier work of the first three authors where a notion of congruence modules in higher codimension is introduced. The main new results are a criterion for detecting regularity of local rings in terms of congruence…

We study the homological behavior of modules over local rings modulo exact zero-divisors. We obtain new results which are in some sense "opposite" to those known for modules over local rings modulo regular elements.

Let $R$ be an associative ring with identity. This paper investigates the structure of the monomorphism category of large $R$-modules and establishes connections with the category of contravariant functors defined on finitely presented…

Let $\varphi\colon R\rightarrow A$ be a ring homomorphism, where $R$ is a commutative noetherian ring and $A$ is a finite $R$-algebra. We provide criteria for detecting the ascent and descent of Gorenstein homological properties. %As an…

Let $R$ be a ring with unity, $\sigma$ an endomorphism of $R$ and $M_R$ a right $R$-module. In this paper, we continue studding $\sigma$-rigid modules that were introduced by Gunner et al. \cite{generalized/rigid}. We give some results on…

For homomorphism K-->S of commutative rings, where K is Gorenstein and S is essentially of finite type and flat as a K-module, the property that all non-trivial fiber rings of K-->S are Gorenstein is characterized in terms of properties of…