Factorization properties of Krull monoids with infinite class group

Wolfgang Hassler¹

¹ Institut für Mathematik Karl-Franzens-Universität Graz Heinrichstraße 36/4 A-8010 Graz, Austria

Colloquium Mathematicum, Tome 92 (2002) no. 2, pp. 229-242

Résumé

{For a non-unit $a$ of an atomic monoid $H$ we call $$L_H(a) = \{k\in {\mathbb N} \mid a = u_1 \ldots u_k \hbox{ with irreducible } u_i\in H\}$$ the set of lengths of $a$. Let $H$ be a Krull monoid with infinite divisor class group such that each divisor class is the sum of a bounded number of prime divisor classes of $H$. We investigate factorization properties of $H$ and show that $H$ has sets of lengths containing large gaps. Finally we apply this result to finitely generated algebras over perfect fields with infinite divisor class group.

Détail

DOI : 10.4064/cm92-2-7

Keywords: non unit atomic monoid call mathbb mid ldots hbox irreducible set lengths krull monoid infinite divisor class group each divisor class sum bounded number prime divisor classes investigate factorization properties has sets lengths containing large gaps finally apply result finitely generated algebras perfect fields infinite divisor class group