On congruence half-factorial Krull monoids with cyclic class group

Abstract : We carry out a detailed investigation of congruence half-factorial Krull monoids with finite cyclic class group and related problems. Specifically, we determine precisely all relatively large values that can occur as a minimal distance of a Krull monoid with finite cyclic class group, as well as the exact distribution of prime divisors over the ideal classes in these cases. Our results apply to various classical objects, including maximal orders and certain semi-groups of modules. In addition, we present applications to quantitative problems in factorization theory. More specifically, we determine exponents in the asymptotic formulas for the number of algebraic integers whose sets of lengths have a large difference.
Document type :
Preprints, Working Papers, ...
Liste complète des métadonnées

Cited literature [41 references]  Display  Hide  Download

Contributor : Wolfgang Schmid <>
Submitted on : Sunday, September 3, 2017 - 8:33:20 PM
Last modification on : Wednesday, March 27, 2019 - 4:10:22 PM
Document(s) archivé(s) le : Monday, December 11, 2017 - 6:14:52 PM


Files produced by the author(s)


  • HAL Id : hal-01580928, version 1
  • ARXIV : 1709.00859


Alain Plagne, Wolfgang Schmid. On congruence half-factorial Krull monoids with cyclic class group. 2017. 〈hal-01580928〉



Record views


Files downloads