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

2014/07/08 by Alfred Geroldinger, Geroldinger, Alfred, Wolfgang Schmid +1 · 1 citation
Mathematics · #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.CO

paper · pdf · doi:10.48550/arxiv.1407.1967

Revista Matem{á}tica Iberoamericana, to appear

arxiv created 2015/05/22 · arxiv updated 2015/05/25

Abstract

Let H be a Krull monoid with class group G and suppose that each class contains a prime divisor. Then every element a ∈ H has a factorization into irreducible elements, and the set \mathsf L (a) of all possible factorization lengths is the set of lengths of a. We consider the system \mathcal L (H) = \ \mathsf L (a) | a ∈ H \ of all sets of lengths, and we characterize (in terms of the class group G) when \mathcal L (H) is additively closed under set addition.

Cited by

• An unrestricted notion of the finite factorization property

Related

• A characterization of class groups via sets of lengths
• A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions
• Sets of Lengths
• A characterization of length-factorial Krull monoids
• Systems of sets of lengths: Transfer Krull monoids versus weakly Krull monoids