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

  • Alfred Geroldinger

    Universität Graz, Austria
  • Wolfgang Alexander Schmid

    Université Paris 13, Villetaneuse, France

Abstract

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

Cite this article

Alfred Geroldinger, Wolfgang Alexander Schmid, The system of sets of lengths in Krull monoids under set addition. Rev. Mat. Iberoam. 32 (2016), no. 2, pp. 571–588

DOI 10.4171/RMI/895