VeranstaltungsortI.2.01Veranstalter Institut für MathematikBeschreibungFor a domain D with quotient field K, the ring of integer-valued polynomials on D,Int(D) = {f in K | for all a in D, f(a) in D }in general does not have unique factorization of elements. In this talk, we discuss non-unique factorizations in Int(Z) where Z is the ring of integers.We present two main results. First, for any finite multiset N of natural numbers greater than 1, there exists a polynomial f in Int(Z) which has exactly |N| essentially different factorizations of the prescribed lengths.In particular, this implies that every finite non-empty set N of natural numbers greater than1 occurs as a set of lengths of a polynomial f in Int(Z). Second, we show that the multiplicative monoid of Int(Z) is not a transfer Krull monoid.Furthermore, we show that both results hold in Int(D) where D is a Dedekind domain with infinitely maximal ideals of finite index.Vortragende(r)Sarah Nakato (TU GRAZ)KontaktSenka Haznadar (senka.omerhodzic@aau.at)