Unions of sets of lengths.

DOI10.7169/facm/1229696561zbMath1228.20046OpenAlexW2080496329MaRDI QIDQ1038632

Alfred Geroldinger, Michael Freeze

Publication date: 18 November 2009

Published in: Functiones et Approximatio. Commentarii Mathematici (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.facm/1229696561

zbMATH Keywords

Krull monoidsnon-unique factorizationsatomic monoidsfactorization lengthssets of lengths of factorizationsorders in algebraic number fields

Mathematics Subject Classification ID

Commutative semigroups (20M14) Units and factorization (11R27) Free semigroups, generators and relations, word problems (20M05) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Arithmetic theory of semigroups (20M13)

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Cites Work

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• Factorization problems in semigroups
• Factorization in Dedekind domains with finite class group
• Zero-sum problems in finite Abelian groups: a survey
• On the asymptotic behavior of unions of sets of lengths in atomic monoids.
• A realization theorem for sets of lengths
• On products of \(k\) atoms.
• Non-unique factorizations of algebraic integers
• On non-unique factorizations into irreducible elements
• On the lengths of factorizations of elements in an algebraic number ring
• Generalized sets of lengths
• Local tameness of \(v\)-Noetherian monoids.
• Finite abelian groups and factorization problems