The system of sets of lengths in Krull monoids under set addition

DOI10.4171/RMI/895zbMath1417.11007arXiv1407.1967MaRDI QIDQ726770

Alfred Geroldinger, Wolfgang Alexander Schmid

Publication date: 14 July 2016

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.1967

zbMATH Keywords

maximal orderszero-sum sequencesKrull monoidssets of lengthsminimal sets of distances

Mathematics Subject Classification ID

Commutative semigroups (20M14) Divisibility and factorizations in commutative rings (13A05) Inverse problems of additive number theory, including sumsets (11P70) Arithmetic theory of semigroups (20M13) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items

Increasing positive monoids of ordered fields are FF-monoids ⋮ A characterization of class groups via sets of lengths. II. ⋮ Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules ⋮ Systems of sets of lengths of Puiseux monoids ⋮ On the local k-elasticities of Puiseux monoids ⋮ Sets of lengths in atomic unit-cancellative finitely presented 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 set of minimal distances in Krull monoids ⋮ Factorization theory in commutative monoids

Cites Work

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• A construction of integer-valued polynomials with prescribed sets of lengths of factorizations
• The catenary degree of Krull monoids. I
• 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
• Arithmetic of seminormal weakly Krull monoids and domains
• A realization theorem for sets of lengths
• Structural additive theory. Based on courses given at Karl-Franzens-Universität Graz, Austria, 2008--2012
• Non-commutative Krull monoids: a divisor theoretic approach and their arithmetic.
• Factorizations of upper triangular matrices
• The set of minimal distances in Krull monoids
• Factorization in the self-idealization of a PID
• Addition Theorems in Acyclic Semigroups
• Factorization in Krull monoids with infinite class group
• Direct-sum decompositions of modules with semilocal endomorphism rings
• Factorization Theory and Decompositions of Modules
• Krull domains of generalized power series

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