On congruence half-factorial Krull monoids with cyclic class group

Alain Plagne (1) , Wolfgang Schmid (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 LAGA - Laboratoire Analyse, Géométrie et Applications

We carry out a detailed investigation of congruence half-factorial Krull monoids of various orders 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.

Mots clés: minimal distance; block monoid; set of lengths; factorization; half-factorial; zero-sum sequence; Krull monoid; Dedekind domain

Domaines: Théorie des nombres [math.NT]; Algèbre commutative [math.AC]

Alain Plagne, Wolfgang Schmid. On congruence half-factorial Krull monoids with cyclic class group. Journal of Combinatorial Algebra, 2019, 3 (4), pp.331-400. ⟨10.4171/jca/34⟩. ⟨hal-01580928v2⟩