Factorizations in Int(D) where D is a Dedekind domain with infinitely...

Non-unique factorization of elements into irreducibles has been observed in the ring of integer-valued polynomials and its generalizations. We show that all finite (multi-)sets of natural numbers greater than 1 occur as (multi-)sets of lengths of a polynomial in Int(D) where D is a Dedekind domain with infinitely many maximal ideals all of whose residue fields are finite. For given integers 1 < m_1 ≤ . . . ≤ m_n we can explicitly construct an element f oh Int(D) which has exactly n essentially different factorizations of lengths m_1, ...,  m_n . In this talk, we speak about the construction techniques and consequences. This is joint work with S. Frisch and S. Nakato.