2020/12/23 by Grynkiewicz, David J.
#06A11 #11B75 #11H06 #11R27 #13A05 #13F05 #20M13 #52A20 #52A23 #52A37 #52C07 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2012.12757
Our motivating goal is factorization in Krull Domains H with finitely generated class group G. The elasticity ρ(H) is the maximal number of atoms in any re-factorization of a product of k atoms. The elasticities are the same as those of a combinatorial monoid of zero-sum sequences B(G0), where G0⊆ G are the classes with height one primes. We characterize when finite elasticity holds for any Krull Domain with finitely generated class group. Our results are valid for the more general class of Transfer Krull Monoids (over a subset G0 of a finitely generated abelian group G). We show there is a minimal s≤ (d+1)m, where d is the torsion free rank and m is the torsion exponent, such that ρs(H)