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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 12 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1373636689

Digital Object Identifier
doi:10.1215/ijm/1373636689

Mathematical Reviews number (MathSciNet)
MR3082874

Zentralblatt MATH identifier
1279.20072

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

Citation

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. https://projecteuclid.org/euclid.ijm/1373636689


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