相关论文: The reduction number of canonical ideals

The purpose of this paper is to characterize one-dimensional local domains, or more in general reduced, in terms of its Macaulay's inverse system. This leads to study almost finitely generated modules in the divided power ring. We…

Let $(R,\fm)$ be a commutative Noetherian local ring and let $M$ be an $R$-module which is a relative Cohen-Macaulay with respect to a proper ideal $\fa$ of $R$ and set $n:=\h_{M}\fa$. We prove that $\ind M<\infty$ if and only if…

The aim of this paper is to extend Cohen structure theorem beyond local rings. Both Cohen structure theorem and Nagata's generalization of it are special cases of our results. We investigate for which rings $R$ there exists a maximal ideal…

We develop the theory of trace modules up to isomorphism and explore the relationship between preenveloping classes of modules and the property of being a trace module, guided by the question of whether a given module is trace in a given…

Let $R$ be a complete local Gorenstein ring of dimension one, with maximal ideal m. We show that if $M$ is a Cohen-Macaulay $R$-module which begins an AR-sequence, then this sequence is produced by a particular endomorphism of m…

We begin the study of the notion of diameter of an ideal I of a polynomial ring S over a field, an invariant measuring the distance between the minimal primes of I. We provide large classes of Hirsch ideals, i.e. ideals with diameter not…

A commutative noetherian local ring $(R,\mathfrak{m})$ is Gorenstein if and only if every parameter ideal of $R$ is irreducible. Although irreducible parameter ideals may exist in non-Gorenstein rings, Marley, Rogers, and Sakurai show there…

Let $R$ be a polynomial ring over a field. We introduce the concept of sequentially almost Cohen-Macaulay modules and describe the extremal rays of the cone of local cohomology tables of finitely generated graded $R$-modules which are…

In the context of modeling biological systems, it is of interest to generate ideals of points with a unique reduced Groebner basis, and the first main goal of this paper is to identify classes of ideals in polynomial rings which share this…

We introduce quasi-Gorenstein morphisms of commutative local dg-algebras and use a Gorenstein version of the virtually small property to characterize them, a result which is new even for homomorphisms of local rings. In a different…

We notice the connection between almost Cohen-Macaulay rings and the Cohen-Macaulay defect. We introduce a Serre-type condition for modules, that is connected to the Cohen-Macaulay defect in the same way that the condition $(S_n)$ is…

This is the second paper in a series of three papers. In the first paper of the series, "Artinian Gorenstein algebras with linear resolutions", (arXiv:1306.2523, J. of Algebra, to appear) we prove that it is possible to give the minimal…

We define the concept of a doset Hibi ring and a generalized doset Hibi ring which are subrings of a Hibi ring and are normal affine semigrouprings. We apply the theory of (generalized) doset Hibi rings to analyze the rings of absolute…

The question of when the Rees algebra ${\mathcal R} (I)= \bigoplus_{n \ge 0}I^n$ of $I$ is an almost Gorenstein graded ring is explored, where $R$ is a two-dimensional regular local ring and $I$ a contracted ideal of $R$. It is known that…

The main aim of this paper is to classify Ulrich ideals and Ulrich modules over two-dimensional Gorenstein rational singularities (rational double points) from a geometric point of view. To achieve this purpose, we introduce the notion of…

We obtain various characterizations of commutative Noetherian local rings $(R, \fm)$ in terms of homological dimensions of certain finitely generated modules. For example, we establish that $R$ is Gorenstein if the Gorenstein injective…

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…

Relations between Gorenstein derived categories, Gorenstein defect categories and Gorenstein stable categories are established. Using these, the Gorensteinness of an algebra $A$ and invariants with respect to recollements of the bounded…

In this article we investigate when a complete ideal in a two-dimensional regular local ring is a multiplier ideal of some ideal with an integral multiplying parameter. In particular, we show that this question is closely connected to the…

We answer a question of Celikbas, Dao, and Takahashi by establishing the following characterization of Gorenstein rings: a commutative noetherian local ring $(R,\mathfrak m)$ is Gorenstein if and only if it admits an integrally closed…