Geodesic
Factorization in Krull monoids with infinite class group
Colloquium Mathematicum, Tome 80 (1999) no. 1, pp. 23-30
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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 $h=u_1·...· u_k$ for some irreducible elements $u_i$, (ii) k ∈ L. 
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Florian Kainrath. Factorization in Krull monoids with infinite class group. Colloquium Mathematicum, Tome 80 (1999) no. 1, pp. 23-30. doi: 10.4064/cm-80-1-23-30

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