Sets of minimal distances and characterizations of class groups of Krull monoids

DOI10.1007/s11139-016-9873-2zbMath1426.11005arXiv1606.08039OpenAlexW3100156019WikidataQ59607446 ScholiaQ59607446MaRDI QIDQ1743625

Qinghai Zhong

Publication date: 13 April 2018

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.08039

zbMATH Keywords

class groupsDavenport constantzero-sum sequencesKrull monoidssets of lengthsarithmetical characterizations

Mathematics Subject Classification ID

Units and factorization (11R27) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Divisibility and factorizations in commutative rings (13A05) Arithmetic theory of semigroups (20M13) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (12)

On product-one sequences over dihedral groups ⋮ A characterization of class groups via sets of lengths ⋮ Sets of Lengths ⋮ A characterization of finite abelian groups via sets of lengths in transfer Krull monoids ⋮ Sets of arithmetical invariants in transfer Krull monoids ⋮ On the incomparability of systems of sets of lengths ⋮ Systems of Sets of Lengths: Transfer Krull Monoids Versus Weakly Krull Monoids ⋮ Long sets of lengths with maximal elasticity ⋮ Puiseux monoids and transfer homomorphisms ⋮ Factorization theory in commutative monoids ⋮ Which sets are sets of lengths in all numerical monoids? ⋮ A characterization of length-factorial Krull monoids

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multiplicative ideal theory and factorization theory. Commutative and non-commutative perspectives. Selected papers based on the presentations at the meeting `Arithmetic and ideal theory of rings and semigroups', Graz, Austria, September 22--26, 2014
• The catenary degree of Krull monoids. I
• Monoids of modules and arithmetic of direct-sum decompositions.
• Every divisor class of Krull monoid domains contains a prime ideal
• The system of sets of lengths in Krull monoids under set addition
• Combinatorial number theory and additive group theory. With a foreword by Javier Cilleruelo, Marc Noy and Oriol Serra (Coordinators of the DocCourse)
• 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.
• Chains of factorizations and sets of lengths
• Zero-sumfree sequences in cyclic groups and some arithmetical application
• A realization theorem for sets of lengths in numerical monoids
• Structural additive theory. Based on courses given at Karl-Franzens-Universität Graz, Austria, 2008--2012
• On congruence half-factorial Krull monoids with cyclic class group
• Differences in sets of lengths of Krull monoids with finite class group.
• A characterization of class groups via sets of lengths. II.
• Sets of lengths in maximal orders in central simple algebras.
• The set of minimal distances in Krull monoids
• The set of distances in Krull monoids
• On minimal distances in Krull monoids with infinite class group
• THE CATENARY DEGREE OF KRULL MONOIDS II
• Krull domains of generalized power series

This page was built for publication: Sets of minimal distances and characterizations of class groups of Krull monoids