The set of minimal distances in Krull monoids

DOI10.4064/aa7906-1-2016zbMath1360.20053arXiv1404.2873OpenAlexW3105568822MaRDI QIDQ2809363

Alfred Geroldinger, Qinghai Zhong

Publication date: 27 May 2016

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.2873

zbMATH Keywords

zero-sum sequencesKrull monoidsnon-unique factorizationscross number

Mathematics Subject Classification ID

Units and factorization (11R27) Divisibility and factorizations in commutative rings (13A05) Arithmetic theory of semigroups (20M13) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (18)

On length densities ⋮ The set of distances in seminormal weakly Krull monoids ⋮ On product-one sequences over dihedral groups ⋮ A characterization of class groups via sets of lengths ⋮ A characterization of class groups via sets of lengths. II. ⋮ Sets of Lengths ⋮ A characterization of finite abelian groups via sets of lengths in transfer Krull monoids ⋮ On the incomparability of systems of sets of lengths ⋮ On Dedekind domains whose class groups are direct sums of cyclic groups ⋮ On divisor-closed submonoids and minimal distances in finitely generated monoids ⋮ Systems of Sets of Lengths: Transfer Krull Monoids Versus Weakly Krull Monoids ⋮ Sets of minimal distances and characterizations of class groups of Krull monoids ⋮ A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions ⋮ Long sets of lengths with maximal elasticity ⋮ The system of sets of lengths in Krull monoids under set addition ⋮ On congruence half-factorial Krull monoids with cyclic class group ⋮ On half-factoriality of transfer Krull monoids ⋮ On transfer homomorphisms of Krull monoids

Cites Work

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• Monoids of modules and arithmetic of direct-sum decompositions.
• Factorization theory: from commutative to noncommutative settings.
• Every divisor class of Krull monoid domains contains a prime ideal
• The system of sets of lengths in Krull monoids under set addition
• Arithmetic of seminormal weakly Krull monoids and domains
• A realization theorem for sets of lengths
• Arithmetical characterization of class groups of the form \(\mathbb Z/n\mathbb Z\oplus\mathbb Z/n\mathbb Z\) via the system of sets of lengths.
• Zero-sumfree sequences in cyclic groups and some arithmetical application
• On large half-factorial sets in elementary \(p\)-groups: maximal cardinality and structural char\-ac\-ter\-i\-zation.
• A realization theorem for sets of lengths in numerical monoids
• Differences in sets of lengths of Krull monoids with finite class group.
• Sets of lengths in maximal orders in central simple algebras.
• On the maximal cardinality of half-factorial sets in cyclic groups
• On minimum delta set values in block monoids over cyclic groups.
• Two conjectures on an addition theorem
• A structure theory for small sum subsets
• The set of distances in Krull monoids
• On minimal distances in Krull monoids with infinite class group
• Inverse zero-sum problems and algebraic invariants
• Congruence monoids
• A quantitative aspect of non-unique factorizations: the Narkiewicz constants III
• Factorization Theory and Decompositions of Modules
• On the index of sequences over cyclic groups
• Periods of sets of lengths: a quantitative result and an associated inverse problem
• On delta sets and their realizable subsets in Krull monoids with cyclic class groups
• Krull domains of generalized power series

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