Affine semigroups having a unique Betti element
Pedro A. Garc\'ia-S\'anchez, Ignacio Ojeda, Jos\'e Carlos Rosales
TL;DR
This paper characterizes affine semigroups with a single Betti element and computes related non-unique factorization invariants, with specific focus on numerical semigroups.
Contribution
It provides a complete characterization of affine semigroups with one Betti element and computes key invariants, extending to numerical semigroups.
Findings
Characterization of affine semigroups with a unique Betti element
Calculation of non-unique factorization invariants for these semigroups
Application of results to numerical semigroups
Abstract
We characterize affine semigroups having one Betti element and we compute some relevant non-unique factorization invariants for these semigroups. As an example, we particularize our description to numerical semigroups.
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