Uniquely presented finitely generated commutative monoids

Details Uniquely presented finitely generated commutative monoids Uniquely presented finitely generated commutative monoids

2009-07-24

arxiv.org/abs/0907.4241v2

Pacific J. Math. 248 (2010), no. 1, 91--105

Mathematics

Commutative Algebra

13 pages, typos corrected, references updated

Scientific paper

10.2140/pjm.2010.248.91

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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