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

Alfred Geroldinger ^[1] ; Wolfgang A. Schmid ^[2]
1. [1] University of Graz
  
  University of Graz
  
  Graz, Austria
2. [2] Université Paris
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 32, Nº 2, 2016, págs. 571-588
Idioma: inglés
DOI: 10.4171/RMI/895
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Resumen
- 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 L(a) of all possible factorization lengths for aa is the set of lengths of aa. We consider the system L(H)={L(a)∣a∈H} of all sets of lengths, and we characterize (in terms of the class group G) when L(H) is additively closed under set addition.