Hilbert Functions play major roles in Algebraic Geometry and Commutative Algebra, and are
becoming increasingly important also in Computational Algebra. They capture many useful …

This is a survey paper on commutative Koszul algebras and Castelnuovo-Mumford
regularity. Koszul algebras, originally introduced by Priddy, are graded K-algebras R whose …

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We introduce the concept of homogeneous numerical semigroups and show that all
homogeneous numerical semigroups with Cohen–Macaulay tangent cones are of …

In this paper, we give a necessary and sufficient condition for the Cohen-Macaulayness of
the associated graded ring of a simplicial affine semigroup using Gröbner basis. We …

Let $ I $ be a homogeneous ideal in a polynomial ring $ P $ over a field. By Macaulay's
Theorem there exists a lexicographic ideal $ L=\operatorname {Lex}(I) $ with the same …

Hilbert functions of Cohen–Macaulay local rings Page 190 Contemporary Mathematics Volume
555 , 2011 Hilbert Functions of Cohen-Macaulay local rings Maria Evelina Rossi Abstract. This …

Let A (C) be the coordinate ring of a monomial curve C⊆ An corresponding to the numerical
semigroup S minimally generated by a sequence a0,…, an. In the literature, little is known …

For instance if n= 3 the terms of degree 3 of R are ordered as follows: and any term of
degree three is smaller than any term of degree 4. It makes sense, therefore, to talk about a …

We study the minimal free resolution of the tangent cone of Gorenstein monomial curves in
affine 4-space. We give the explicit minimal free resolution of the tangent cone of …