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

TL;DR

This paper explores the structure of divisor-closed submonoids in finitely generated monoids, providing geometric characterizations and an algorithm to compute minimal distances, advancing understanding in algebraic and geometric aspects of monoids.

Contribution

It offers a geometric characterization of divisor-closed submonoids in affine semigroups and introduces an algorithm for computing minimal distances in finitely generated monoids.

Findings

Geometric characterization of divisor-closed submonoids in affine semigroups

Algorithm for computing the set of minimal distances

Enhanced understanding of the lattice structure of submonoids

Abstract

We study the lattice of divisor-closed submonoids of finitely generated cancellative commutative monoids. In case the monoid is an affine semigroup, we give a geometrical characterization of such submonoids in terms of its cone. Finally, we use our results to give an algorithm for computing $\Delta^*(H)$ the set of minimal distance of $H$.