Related papers: Simplicial affine semigroups with monomial minimal…
In this paper, we study simplicial complexes whose Stanley-Reisner rings are almost Gorenstein and have $a$-invariant zero. We call such a simplicial complex an almost Gorenstein* simplicial complex. To study the almost Gorenstein*…
In this paper, we deal with the problem of uniqueness of minimal system of binomial generators of a semigroup ideal. Concretely, we give different necessary and/or sufficient conditions for uniqueness of such minimal system of generators.…
In this note we characterize the affine semigroup rings K[S] over an arbitrary field K that satisfy condition R_l of Serre. Our characterization is in terms of the face lattice of the positive cone pos(S) of S. We start by reviewing some…
This paper investigates the relation between the almost Gorenstein properties for graded rings and for local rings. Once $R$ is an almost Gorenstein graded ring, the localization $R_M$ of $R$ at the graded maximal ideal $M$ is almost…
We develop a new technique for studying monomial ideals in the standard polynomial rings $A[X_1,\ldots,X_d]$ where $A$ is a commutative ring with identity. The main idea is to consider induced ideals in the semigroup ring…
Judith Sally proved in 1980 that the associated graded ring of one-dimensional Gorenstein local rings of multiplicity $e$ and embedding dimension $e-2$ are Cohen-Macaulay. She showed that the defining ideal of the associated graded ring of…
In this article, applying the quasi-Gorenstein analogous of the Ulrich's deformation of certain Gorenstein rings we show that some homological conjectures, including the Monomial Conjecture, Big Cohen-Macaulay Algebra Conjecture as well as…
We describe the typical homological properties of monomial ideals defined by random generating sets. We show that, under mild assumptions, random monomial ideals (RMI's) will almost always have resolutions of maximal length; that is, the…
In this article, we give the explicit minimal free resolution of the associated graded ring of certain affine monomial curves in affine 4-space based on the standard basis theory. As a result, we give the minimal graded free resolution and…
This paper contains two theorems concerning the theory of maximal Cohen--Macaulay modules. The first theorem proves that certain Ext groups between maximal Cohen--Macaulay modules $M$ and $N$ must have finite length, provided only finitely…
A concrete description of all graded maximal Cohen-Macaulay modules of rank one and two over the affine cone of the simple node (a non-isolated singularity) is given. For this purpose we construct an alghoritm that provides extensions of…
We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal…
A semidualizing module is a generalization of Grothendieck's dualizing module. For a local Cohen-Macaulay ring $R$, the ring itself and its canonical module are always realized as (trivial) semidualizing modules. Reasonably, one might…
Let $(A,\mathfrak{m})$ be a Gorenstein local ring and let $M$ be a finitely generated Cohen Macaulay $A$ module. Let $G(A)=\bigoplus_{n\geq 0}\mathfrak{m}^n/\mathfrak{m}^{n+1}$ be the associated graded ring of $A$ and $G(M)=\bigoplus_{n\geq…
Our main purpose is to give multiple examples for using the available implementations for computing the normalization of an affine ring, computing the minimial generators of the normalization as an algebra over the original ring and…
We explore the behavior of the sectional genera of certain primary ideals in Noetherian local rings. In this paper, we provide characterizations of a Cohen-Macaulay local ring in terms of the sectional genera, the Cohen-Macaulay type, and…
Here we characterize regular and completely regular ordered semigroups by their minimal bi-ideals. A minimal bi-ideal is expressed as a product of a minimal right ideal and a minimal left ideal. Furthermore, we show that every bi-ideal in a…
In this article, we first prove that the type of an affine semigroup ring is equal to the number of maximal elements of the Ap\'ery set with respect to the set of exponents of the monomials, which form a maximal regular sequence. Further,…
We construct the minimal resolutions of three classes of monomial ideals: dominant, 1-semidominant, and 2-semidominant ideals. The families of dominant and 1-semidominant ideals extend those of complete and almost complete intersections. We…
We study arithmetic properties of tangent cones associated to affine monomial curves, using the concept of gluing. In particular we characterize the Cohen-Macaulay and Gorenstein properties of tangent cones of some families of monomial…