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

• Alfred Geroldinger ^[1] ; Wolfgang Alexander Schmid ^[2]
  1. [1] University of Graz

     University of Graz

     Graz, Austria

     
  2. [2] Paris 13 University

     Paris 13 University

     Arrondissement de Saint-Denis, Francia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 1, 2021, págs. 293-316
• Idioma: inglés
• DOI: 10.4171/rmi/1207
• Enlaces
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• Resumen

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