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

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 Δ⁎(H), t...

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Bibliographic Details
Published inJournal of symbolic computation Vol. 93; pp. 230 - 245
Main Authors García-García, J.I., Marín-Aragón, D., Moreno-Frías, M.A.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.07.2019
Subjects
Archimedean component
Cancellative monoid
Commutative monoid
Divisor-closed submonoid
Finitely generated monoid
Non-unique factorizations
Polyhedral cone
Set of minimal distances
Finitely generated monoid
Divisor-closed submonoid
20M14
20M13
Commutative monoid
52B11
Set of minimal distances
13A05
Non-unique factorizations
Polyhedral cone
Archimedean component
Cancellative monoid
11R27
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Summary: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 Δ⁎(H), the set of minimal distances of H.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2018.06.008