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Factorization properties of Krull monoids with infinite class group

Wolfgang Hassler — 2002

Colloquium Mathematicae

For a non-unit a of an atomic monoid H we call $L_{H} (a) = k \in ℕ | a = u ₁ . . . u_{k} w i t h i r r e d u c i b l e u_{i} \in H$ 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.

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