A numerical semigroup is a subset of the set N of nonnegative integers that is closed under
addition, contains 0 and whose complement in N is finite. The smallest positive integer …

A family of quotient rings of the Rees algebra associated to a commutative ring is studied.
This family generalizes both the classical concept of idealization by Nagata and a more …

For a reduced one-dimensional complete local $ k $-algebra $ R $, Huneke et al.(Res. Math.
Sci., 8 (4), paper no. 60, 2021) introduced an important invariant, the reduced type. In this …

Let ng be the number of numerical semigroups of genus g. We present an approach to
compute ng by using even gaps, and the question: Is it true that n g+ 1> ng? is investigated …

In this paper we solve a problem posed by ME Rossi: Is the Hilbert function of a Gorenstein
local ring of dimension one not decreasing? More precisely, for any integer h> 1, h∉{14+ 22 …

Starting with a commutative ring RR and an ideal II, it is possible to define a family of rings R
(I) a, b R(I)_a,b, with a, b∈ R a,b∈R, as quotients of the Rees algebra⊕ n≥ 0 I ntn …

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 propose the notion of GAS numerical semigroup which generalizes both almost
symmetric and 2-AGL numerical semigroups. Moreover, we introduce the concept of almost …

Motivated by the change-making problem, we extend the notion of greediness to sets of
positive integers not containing the element 1, and from there to numerical semigroups. We …

It is proved that the number of numerical semigroups with a fixed number n of star operations
is finite if n> 1. The result is then extended to the class of analytically irreducible residually …