J. I. García-García

Systems of Inequalities and Numerical Semigroups

A one-to-one correspondence is described between the setS(m) of numerical semigroups with multiplicity m and the set of non-negative integer solutions of a system of linear Diophantine inequalities. This correspondence infers in S(m) a semigroup structure and the resulting semigroup is isomorphic to a subsemigroup of Nm−1. Finally, this result is particularized to the symmetric case.

Computing the elasticity of a Krull monoid

Abstract If S is a Krull monoid with finitely generated divisor class group such that only finitely many divisor classes of S contain prime divisors, then we construct an algorithm to compute the elasticity of S .

Affine convex body semigroups

In this paper we present a new class of semigroups called convex body semigroups which are generated by convex bodies of ℝk. They generalize to arbitrary dimension the concept of proportionally modular numerical semigroups of Rosales et al. (J. Number Theory 103, 281–294, 2003). Several properties of these semigroups are proven. Affine convex body semigroups obtained from circles and polygons of ℝ2 are characterized. The algorithms for computing minimal system of generators of these semigroups are given. We provide the implementation of some of them.

PRESENTATIONS OF FINITELY GENERATED SUBMONOIDS OF FINITELY GENERATED COMMUTATIVE MONOIDS

We give an algorithmic method for computing a presentation of any finitely generated submonoid of a finitely generated commutative monoid. We use this method also for calculating the intersection of two congruences on ℕp and for deciding whether or not a given finitely generated commutative monoid is t-torsion free and/or separative. The last section is devoted to the resolution of some simple equations on a finitely generated commutative monoid.

An extension of Wilf’s conjecture to affine semigroups

Let

On decomposable semigroups and applications

\mathcal {C}\subset \mathbb {Q}^p_+

On divisor-closed submonoids and minimal distances in finitely generated monoids

C⊂Q+p be a rational cone. An affine semigroup