Uniquely presented finitely generated commutative monoids
Pedro A. Garcia-Sanchez, Ignacio Ojeda
TL;DR
This paper characterizes when finitely generated commutative monoids are uniquely presented, providing conditions, construction methods via gluing, and descriptions for specific numerical semigroup families.
Contribution
It offers necessary and sufficient conditions for unique presentation, introduces a gluing construction method, and describes uniquely presented elements in key numerical semigroup families.
Findings
Conditions for unique presentation in finitely generated monoids
A gluing-based construction method for such monoids
Descriptions of uniquely presented elements in numerical semigroups
Abstract
A finitely generated commutative monoid is uniquely presented if it has only a minimal presentation. We give necessary and sufficient conditions for finitely generated, combinatorially finite, cancellative, commutative monoids to be uniquely presented. We use the concept of gluing to construct commutative monoids with this property. Finally for some relevant families of numerical semigroups we describe the elements that are uniquely presented.
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