We characterize numerical semigroups for which the divisibility poset of its ideal class monoid is a lattice, and study the irreducible elements of such a lattice with respect to meet and join in this poset, as well as with respect to union and intersection.
When the divisibility poset of the ideal class monoid of a numerical semigroup is a lattice
Bonzio S.;
2026-01-01
Abstract
We characterize numerical semigroups for which the divisibility poset of its ideal class monoid is a lattice, and study the irreducible elements of such a lattice with respect to meet and join in this poset, as well as with respect to union and intersection.
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