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
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Abstract

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