Related papers: The Cohen-Macaulay property in derived commutative…
We study the converse of a theorem of Butler and Auslander-Reiten. We show that a Cohen-Macaulay local ring with an isolated singularity has only finitely many isomorphism classes of indecomposable summands of syzygies of Cohen-Macaulay…
In Commutative Algebra structure results on minimal free resolutions of Gorenstein modules are of classical interest. We define Gorenstein modules of finite length over the weighted polynomial ring via symmetric matrices in divided powers.…
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 introduce the notion of a lim Cohen-Macaulay sequence of modules. We prove the existence of such sequences in positive characteristic, and show that their existence in mixed characteristic implies the long open conjecture about…
Let $A \bowtie^{f,g} (J,J')$ be the bi--amalgamation of a commutative ring $A$ with $(B,C)$ along the ideals $(J,J')$ with respect to the ring homomorphisms $(f,g)$. In this article, we study the basic homological properties of the…
Let $R$ be a Noetherian local ring and $I$ an $R$-ideal. It is well-known that if the associated graded ring $\gr_I(R)$ is Cohen-Macaulay (Gorenstein), then so is $R$, but the converse is not true in general. In this paper we investigate…
In this paper we present characterizations of sequentially Cohen-Macaulay modules in terms of systems of parameters, which are generalizations of well-known results on Cohen-Macaulay and generalized Cohen-Macaulay modules. The sequentially…
We investigate Cohen factorizations of local ring homomorphisms from three perspectives. First, we prove a "weak functoriality" result for Cohen factorizations: certain morphisms of local ring homomorphisms induce morphisms of Cohen…
Over a commutative local Cohen--Macaulay ring, we view and study the category of maximal Cohen--Macaulay modules as a ring with several objects. We compute the global dimension of this category and thereby extend a result of Leuschke to the…
We give a new proof of a recent result due to Mats Andersson and Elizabeth Wulcan, generalizing the local Grothendieck duality theorem. It can also be seen as a generalization of a previous result by Mikael Passare. Our method does not…
In the present paper, it is proved that any complete local domain of mixed characteristic has a weakly almost Cohen-Macaulay algebra in the sense that some system of parameters is a weakly almost regular sequence, which is a notion defined…
In this paper we investigate a property for commutative rings with identity which is possessed by every coherent regular ring and is equivalent to Cohen-Macaulay for Noetherian rings. We study the behavior of this property in the context of…
The aim of this paper is to study the theory of cohomology annihilators over commutative Gorenstein rings. We adopt a triangulated category point of view and study the annihilation of stable category of maximal Cohen-Macaulay modules. We…
In this paper we consider the problem of finding explicitly canonical ideals of one-dimensional Cohen-Macaulay local rings. We show that Gorenstein ideals contained in a high power of the maximal ideal are canonical ideals. In the…
In this paper, we prove that if Cohen-Macaulay local/graded rings $R_1$, $R_2$ and $R$ satisfy certain conditions regarding multiplicity and Cohen-Macaulay type, then almost Gorenstein property of $R$ implies Gorenstein properties for all…
We establish a criterion for the strong $F$-regularity of a (non-Gorenstein) Cohen-Macaulay reduced complete local ring of dimension at least $2$, containing a perfect field of prime characteristic $p$. We also describe an explicit…
The relationships between the invariants and the homological properties of $I$, ${\rm Gin}(I)$ and $I^{\rm lex}$ have been studied extensively over the past decades. A result of A. Conca, J. Herzog and T. Hibi points out some rigid…
Over a Cohen-Macaulay local ring, the minimal number of generators of a maximal Cohen-Macaulay module is bounded above by its multiplicity. In 1984 Ulrich asked whether there always exist modules for which equality holds; such modules are…
Given a Cohen-Macaulay local ring, the cohomology annihilator ideal and the annihilator of the stable category of maximal Cohen-Macaulay modules are two ideals closely related both with each other and the singularities of the ring. Kimura…
Our main goal in this paper is to answer new positive cases of the natural generalized version of Hartshorne's celebrated question on cofiniteness of local cohomology modules, and consequently of Huneke's conjecture on the finiteness of…