Vortrag von Sarah Nakato (TU Graz) im Rahmen des DK – Seminars
Veranstaltungsort
I.2.01
Veranstalter
Institut für Mathematik
Beschreibung
For a domain D with quotient field K, the ring of integer-valued polynomials on D,
Int(D) = {f in K[x] | 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 than
1 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)
Kontakt
Senka Haznadar (senka [dot] omerhodzic [at] aau [dot] at)
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