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Divisibility Relations and -Extremal ideals
Susan M. Cooper, Sabine El Khoury, Sara Faridi +3
A divisibility relation between the generators of a square-free monomial ideal formally encodes the situation when one generator divides the least common multiple of some other gen…
Simplicial resolutions for the second power of square-free monomial ideals
Susan M. Cooper, Sabine El Khoury, Sara Faridi +4
Given a square-free monomial ideal , we define a simplicial complex labeled by the generators of which supports a free resolution of . As a consequence, we obtain (sh…
An Upper Bound for the First Hilbert Coefficient of Gorenstein Algebras and Modules
Sabine El Khoury, Manoj Kummini, Hema Srinivasan
Let be a polynomial ring over a field and a finitely generated graded -module, minimally generated by homogeneous elements of degree zero with a graded…
On the projective dimension of quadric almost complete intersections with low multiplicities
Sabine El Khoury
Let be a polynomial ring over an algebraic closed field and a homogeneous height four prime ideal. We give a finite characterization of the degre…
On the number of generators of ideals defining Gorenstein Artin algebras with Hilbert function
Sabine El Khoury, A. V. Jayanthan, Hema Srinivasan
Let be a graded Gorenstein Artin algebra . Then $I = \ann F$ for some in the divided power algebra . If is a height o…
Bounds for the Multiplicity of Gorenstein algebras
Sabine El Khoury, Manoj Kummini, Hema Srinivasan
We prove upper bounds for the Hilbert-Samuel multiplicity of standard graded Gorenstein algebras. The main tool that we use is Boij-Söderberg theory to obtain a decomposition of th…