Factorization properties of Krull monoids with infinite class group
Tom 92 / 2002
Colloquium Mathematicum 92 (2002), 229-242
MSC: 13F05, 13A05, 13C20, 20M14.
DOI: 10.4064/cm92-2-7
Streszczenie
{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.
