# 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.
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## 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
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