# Betti numbers for numerical semigroup rings

@article{Stamate2016BettiNF, title={Betti numbers for numerical semigroup rings}, author={Dumitru I. Stamate}, journal={arXiv: Commutative Algebra}, year={2016} }

We survey results related to the magnitude of the Betti numbers of numerical semigroup rings and of their tangent cones.

## 16 Citations

Coefficient rings of numerical semigroup algebras

- MathematicsSemigroup Forum
- 2021

Numerical semigroup rings are investigated from the relative viewpoint. It is known that algebraic properties such as singularities of a numerical semigroup ring are properties of a flat numerical…

BETTI NUMBERS FOR CERTAIN COHEN–MACAULAY TANGENT CONES

- MathematicsBulletin of the Australian Mathematical Society
- 2018

We compute Betti numbers for a Cohen–Macaulay tangent cone of a monomial curve in the affine $4$ -space corresponding to a pseudo-symmetric numerical semigroup. As a byproduct, we also show that for…

The generators, relations and type of the Backelin semigroup

- MathematicsCommunications in Algebra
- 2021

Abstract We present an explicit minimal set of generators for the defining ideal of the family of Backelin semigroups and find its Betti numbers. In particular, we compute the type of the semigroup…

Unboundedness of Betti numbers of certain monomial curves in $\mathbb{A}^{4}$

- Mathematics
- 2018

Bresinsky defined a class of monomial curves in $\mathbb{A}^{4}$ with the property that the minimal number of generators or the first Betti number of the defining ideal is unbounded above. We prove…

Type and conductor of simplicial affine semigroups

- Mathematics
- 2022

Abstract We provide a generalization of pseudo-Frobenius numbers of numerical semigroups to the context of the simplicial affine semigroups. In this way, we characterize the Cohen-Macaulay type of…

Canonical trace ideal and residue for numerical semigroup rings

- Mathematics
- 2020

For a numerical semigroup ring $K[H]$ we study the trace of its canonical ideal. The colength of this ideal is called the residue of $H$. This invariant measures how far is $H$ from being symmetric,…

Minimal free resolutions of the tangent cones for Gorenstein monomial curves

- Mathematics
- 2018

The aim of the article is to study the minimal free resolution of the tangent cone of Gorenstein monomial curves in affine 4-space. If C is a non-complete intersection Gorenstein monomial curve that…

Tangent cones of monomial curves obtained by numerical duplication

- MathematicsCollectanea Mathematica
- 2019

Given a numerical semigroup ring $$R=k\llbracket S\rrbracket $$R=k〚S〛, an ideal E of S and an odd element $$b \in S$$b∈S, the numerical duplication $$S \bowtie ^b E$$S⋈bE is a numerical semigroup,…

On the Betti numbers of the tangent cones for Gorenstein monomial curves

- MathematicsTURKISH JOURNAL OF MATHEMATICS
- 2021

Let S denote the numerical semigroup generated by the positive integers n1 < n2 < . . . < nd with gcd(n1, . . . , nd) = 1. Consider the polynomial rings R = k[x1, . . . , xd] and k[t] over the field…

Nearly Gorenstein vs Almost Gorenstein Affine Monomial Curves

- Mathematics
- 2020

We extend some results on almost Gorenstein affine monomial curves to the nearly Gorenstein case. In particular, we prove that the Cohen-Macaulay type of a nearly Gorenstein monomial curve in…

## References

SHOWING 1-10 OF 94 REFERENCES

Genus of numerical semigroups generated by three elements

- Mathematics
- 2011

In this paper we study numerical semigroups generated by three elements. We give a characterization of pseudo-symmetric numerical semigroups. Also, we will give a simple algorithm to get all the…

On the Betti numbers of some semigroup rings

- Mathematics
- 2011

For any numerical semigroup S, there are infinitely many numerical symmetric semigroups T such that S = T/2 (see below for the definition of T/2) is their half. We are studying the Betti numbers of…

On monomial curves and Cohen-Macaulay type

- Mathematics
- 1983

In this paper we characterize the monomial arithmetically Cohen-Macaulay curves in Pd and compute the type of their coordinate ring

On intersections of complete intersection ideals

- Mathematics
- 2016

Abstract We prove that for certain families of toric complete intersection ideals, the arbitrary intersections of elements in the same family are again complete intersections.

On pseudo symmetric monomial curves

- Mathematics
- 2015

ABSTRACT We study monomial curves, toric ideals and monomial algebras associated to 4-generated pseudo symmetric numerical semigroups. Namely, we determine indispensable binomials of these toric…

On free resolutions of some semigroup rings

- Mathematics
- 2012

For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in…

numericalsgps, a GAP package for numerical semigroups

- ACCA
- 2016

The package numericalsgps performs computations with and for numerical and affine semigroups. This manuscript is a survey of what the package does, and at the same time intends to gather the rending…

Almost Gorenstein monomial curves in affine four space

- Mathematics
- 2017

Abstract In this paper, we classify the almost symmetric semigroups of embedding dimension four. And we give minimal systems of generators and minimal free resolutions for the defining ideals of…

Grobner Bases in Commutative Algebra

- Mathematics
- 2011

Polynomial rings and ideals Grobner bases First applications Grobner bases for modules Grobner bases of toric ideals Selected applications in commutative algebra and combinatorics Bibliography Index

Explicit minimal resolution for certain monomial curves

- Mathematics
- 2013

With a view to study problems of smoothability, we construct a minimal free resolution for the coordinate ring of an algebroid monomial curve associated to an $AS$ numerical semigroup (i.e. generated…