In this paper we give necessary and sufficient conditions for the Cohen-Macaulayness of the
tangent cone of a monomial curve in 4-dimensional affine space. We particularly study the …

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 …

We collect some open problems about minimal presentations of numerical semigroups and,
more generally, about defining ideals and free resolutions of their semigroup rings and …

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

In this article we solve the following problem:“The Hilbert function of the local ring of a 4-
generated pseudo-symmetric numerical semigroup is always non-decreasing.” We give a …

Given a one-dimensional Cohen-Macaulay local ring (R, m, k), we prove that it is almost
Gorenstein if and only if m is a canonical module of the ring m: m. Then, we generalize this …

Given a one-dimensional semigroup ring R= k [[S]], in this article we study the behaviour of
the Hilbert function H R. By means of the notion of support of the elements in S, for some …

We study some properties of a family of rings R (I) a, b that are obtained as quotients of the
Rees algebra associated with a ring R and an ideal I. In particular, we give a complete …

We study almost symmetric semigroups generated by odd integers. If the embedding
dimension is four, we characterize when a symmetric semigroup that is not complete …

In this paper we show that a large class of one-dimensional Cohen-Macaulay local rings
$(A,\mathfrak {m}) $ has the property that if $ M $ is a maximal Cohen-Macaulay $ A …