Related papers: Links of prime ideals
We deal with the complete-intersection property of maximally differential ideals. Also, we connect the Gorenstein homology of derivations to the Gorenstein property of the base rings. These equipped with some applications.
We classify connected graphs $G$ whose binomial edge ideal is Gorenstein. The proof uses methods in prime characteristic.
Inspired by Jorgensen et. al., it is proved that if a Cohen--Macaulay local ring $R$ with dualizing module admits a suitable chain of semidualizing $R$--modules of length $n$, then $R\cong Q/(I_1+\cdots+I_n)$ for some Gorenstein ring $Q$…
We study one-dimensional Cohen-Macaulay rings whose trace ideal of the canonical module is as small as possible. In this paper we call such rings far-flung Gorenstein rings. We investigate far-flung Gorenstein rings in relation with the…
To a simplicial complex, we associate a square-free monomial ideal in the polynomial ring generated by its vertex set over a field. We study algebraic properties of this ideal via combinatorial properties of the simplicial complex. By…
This paper investigates the quasi-Gorenstein property of extended Rees algebras associated with the Hilbert filtrations on a Noetherian local ring. We provide necessary and sufficient conditions for the deformation of the quasi-Gorenstein…
The acquisition of the defining equations of Rees algebras is a natural way to study these algebras and allows certain invariants and properties to be deduced. In this paper, we consider Rees algebras of codimension 2 perfect ideals of…
We describe the canonical module of a simplicial affine semigroup ring $\mathbb{K}[S]$ and its trace ideal. As a consequence, we characterize when $\mathbb{K}[S]$ is nearly Gorenstein in terms of arithmetic properties of the semigroup $S$.…
Explicit generating sets are found for all primitive ideals in the generic quantized coordinate rings of the 3x3 special and general linear groups over an arbitrary algebraically closed field. (Previously, generators were only known up to…
We deal with classes of prime ideals whose associated graded ring is isomorphic to the Rees algebra of the conormal module in order to describe the divisor class group of the Rees algebra and to examine the normality of the conormal module.
Inspired by recent work in the theory of central projections onto hypersurfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert--Burch matrix that has a maximal symmetric subblock. We also prove that every…
The aim of this note is to study the class of one dimensional Cohen-Macaulay local rings, $(R, \mathfrak{m})$ say, possessing a canonical ideal $K$ which is a reduction of $\mathfrak{m}$. We call $R$ to have canonical reduction $K$. We show…
Macaulay's Inverse System gives an effective method to construct Artinian Gorenstein k-algebras. To date a general structure for Gorenstein k-algebras of any dimension (and codimension) is not understood. In this paper we extend Macaulay's…
We construct families of prime ideals in polynomial rings for which the number of associated primes of the second power (or higher powers) is exponential in the number of variables in the ring. We give a lower bound on the Ananyan-Hochster…
In this article we first compare the set of elements in the socle of an ideal of a polynomial algebra $K[x_1,\ldots,x_d]$ over a field $K$ that are not in the ideal itself and Macaulay's inverse systems of such polynomial algebras in a…
Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying a special property must be prime. We present a "Prime Ideal Principle" that gives a uniform method of proving such facts, generalizing the…
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…
Starting with a commutative ring $R$ and an ideal $I$, it is possible to define a family of rings $R(I)_{a,b}$, with $a,b \in R$, as quotients of the Rees algebra $\oplus_{n \geq 0} I^nt^n$; among the rings appearing in this family we find…
Polyomino ideals, defined as the ideals generated by the inner $2$-minors of a polyomino, are a class of binomial ideals whose algebraic properties are closely related to the combinatorial structure of the underlying polyomino. We provide a…
While every grade 2 perfect ideal in a regular local ring is linked to a complete intersection ideal, it is known not to be the case for ideals of grade 3. We soften the blow by proving that every grade 3 perfect ideal in a regular local…