Logic Seminar
Mikhail Kotchetov
DePaul University
Primes and Irreducibles in Truncation Integer Parts of Real Closed Fields
Abstract: Berarducci (2000) studied irreducible elements of the ring $k((G^{<0}))\oplus \Z$, which is an integer
part of the power series field $k((G))$ where $G$ is an ordered divisible abelian group and $k$ is an
ordered field. Pitteloud (2001) proved that some of the irreducible elements constructed by Berarducci
are actually prime. Both authors mainly concentrated on the case of archimedean $G$. In this paper, we
study {\it truncation integer parts} of any real closed field and generalize results of Berarducci and
Pitteloud. In particular, we prove that $k((G^{<0}))\oplus\Z$ has (cofinally many) prime elements for
any ordered divisible abelian group $G$. Addressing a question in the paper of Berarducci, we show
that every truncation integer part of a non-archimedean exponential field has a cofinal set of
irreducible elements. (Joint with S. Kuhlmann and D. Biljakovic.)
Note unusal day of the week.
Thursday October 6, 2005 at 4:00 PM in SEO 427