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Uniquely presented
finitely generated commutative monoids
Pedro A. García-Sánchez and Ignacio Ojeda |
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Vol. 248 (2010), No. 1, 91–105
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Abstract |
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A finitely generated commutative monoid is uniquely presented if it has a unique 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. |
Keywords
commutative monoid, affine semigroup, numerical semigroup,
congruences, minimal presentation, Betti numbers,
indispensability, gluing of semigroups
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Mathematical Subject Classification 2000
Primary: 20M14
Secondary: 20M05
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Milestones
Received: 24 July 2009
Revised: 6 May 2010
Accepted: 10 May 2010
Published: 1 October 2010
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Authors |
| Pedro A. García-Sánchez | |
| Departamento de Álgebra Universidad de Granada Av. Fuentenueva, s/n E18071 Granada Spain |
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| http://www.ugr.es/~pedro/ | |
| Ignacio Ojeda | |
| Departamento de Matemáticas Universidad de Extremadura Av. de Elvas, s/n E06071 Badajoz Spain |
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| http://matematicas.unex.es/~ojedamc/ | |
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