Illinois Journal of Mathematics

Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids

V. Blanco, P. A. García-Sánchez, and A. Geroldinger

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Arithmetical invariants—such as sets of lengths, catenary and tame degrees—describe the non-uniqueness of factorizations in atomic monoids. We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids.

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Illinois J. Math., Volume 55, Number 4 (2011), 1385-1414.

First available in Project Euclid: 12 July 2013

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Primary: 20M13: Arithmetic theory of monoids 20M14: Commutative semigroups 13A05: Divisibility; factorizations [See also 13F15]


Blanco, V.; García-Sánchez, P. A.; Geroldinger, A. Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids. Illinois J. Math. 55 (2011), no. 4, 1385--1414. doi:10.1215/ijm/1373636689.

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