JournalsrmiVol. 37, No. 1pp. 293–316

A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions

  • Alfred Geroldinger

    Universität Graz, Austria
  • Wolfgang Alexander Schmid

    Université Paris 13, Villetaneuse, France
A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions cover

A subscription is required to access this article.

Abstract

Let HH be a Krull monoid with finite class group GG and suppose that every class contains a prime divisor. Then sets of lengths in HH have a well-defined structure which depends only on the class group GG. With methods from additive combinatorics we establish a characterization of those class groups GG guaranteeing that all sets of lengths are (almost) arithmetical progressions.

Cite this article

Alfred Geroldinger, Wolfgang Alexander Schmid, A characterization of Krull monoids for which sets of lengths are (almost) arithmetical progressions. Rev. Mat. Iberoam. 37 (2021), no. 1, pp. 293–316

DOI 10.4171/RMI/1207