Some recent results and open problems on sets of lengths of Krull monoids with finite class group

2015/11/25 by Wolfgang Schmid, Schmid, Wolfgang · 4 citations
Mathematics · #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Rings, Modules, and Algebras #math.AC #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1511.08080

arxiv created 2015/11/25 · openalex publication_date 2015/11/25 · arxiv updated 2015/11/26 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28

Abstract

Some of the fundamental notions related to sets of lengths of Krull monoids with finite class group are discussed, and a survey of recent results is given. These include the elasticity and related notions, the set of distances, and the structure theorem for sets of lengths. Several open problems are mentioned.

Cited by

• On minimal product-one sequences of maximal length over the non-abelian group of order pq
• On the structure of length sets with maximal elasticity
• On the system of length sets of power monoids
• The catenary degree of monoids of product-one sequences

Related

• A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions
• A characterization of length-factorial Krull monoids
• A characterization of class groups via sets of lengths
• Systems of sets of lengths: Transfer Krull monoids versus weakly Krull monoids
• The system of sets of lengths in Krull monoids under set addition