Affine semigroups having a unique Betti element

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.

8 pages, 1 figure. To appear in Journal of Algebra and its Applications

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• Squarefree divisor complexes of certain numerical semigroup elements
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• Ordinarization numbers of numerical semigroups