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Factorization in Krull monoids with infinite class group

Florian Kainrath (1999)

Colloquium Mathematicae

Let H be a Krull monoid with infinite class group and such that each divisor class of H contains a prime divisor. We show that for each finite set L of integers ≥2 there exists some h ∈ H such that the following are equivalent: (i) h has a representation $h = u_{1} \cdot . . . \cdot u_{k}$ for some irreducible elements $u_{i}$ , (ii) k ∈ L.