Weakly half-factorial sets in finite abelian groups

DOI10.1515/FORUM.2007.028zbMath1144.20033MaRDI QIDQ5421645

Maciej Radziejewski, Wolfgang Alexander Schmid

Publication date: 24 October 2007

Published in: Forum Mathematicum (Search for Journal in Brave)

zbMATH Keywords

finite Abelian groupsatomsnon-unique factorizationssets of lengthslengths of factorizationscross numbersminimal zero-sum sequencesmonoids of zero-sum sequencesweakly half-factorial sets

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Commutative semigroups (20M14) Units and factorization (11R27) Finite abelian groups (20K01) Special sequences and polynomials (11B83) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Divisibility and factorizations in commutative rings (13A05)

Related Items (6)

Erdős-Zaks all divisor sets. ⋮ A new upper bound for the cross number of finite Abelian groups. ⋮ On congruence half-factorial Krull monoids with cyclic class group ⋮ EZADS inputs which produce half-factorial block monoids. ⋮ On the arithmetic of Krull monoids with finite Davenport constant. ⋮ Factorization theory of root closed monoids of small rank

Cites Work

• Reducible sums and splittable sets
• Factorization in Dedekind domains with finite class group
• A characterization of algebraic number fields with cyclic class group of prime power order
• On non-unique factorizations into irreducible elements
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• The cross number of finite Abelian groups
• An addition theorem and its arithmetical application
• On large half-factorial sets in elementary \(p\)-groups: maximal cardinality and structural char\-ac\-ter\-i\-zation.
• The cross number of finite Abelian groups. III
• On the maximal cardinality of half-factorial sets in cyclic groups
• Ein quantitatives Resultat über Faktorisierungen verschiedener Länge in algebraischen Zahlkörpern. (A quantitative result on factorizations of different length in algebraic number fields)
• Systems of sets of lengths.
• Half factorial domains
• On the distribution of algebraic numbers with prescribed factorization properties
• On the asymptotic behavior of some counting functions
• Congruence monoids
• Systems of sets of lengths. II

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