Naslov
Primes and Irreducibles in Truncation Integer Parts of Real Closed Fields.

Autori
Biljakovic, Darko ; Kochetov, Mikhail ; Kuhlmann, Salma

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Logic in Tehran: Proceedings of a Workshop and Conference on Logic, Algebra, and Arithmetics / A. Enayat, I. Kalantari, and M. Moniri - Los Angeles (CA) : Association of Symbolic Logic, 2005

Skup
Conference on Logic, Algebra, and Arithmetics

Mjesto i datum
, 10.2003

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
real closed fields; irreducibles; primes; integer parts

Sažetak
Berarducci (2000) studied irreducible elements of the ring  ((  0))&copy ; ; ; Z, which is an integer part of the power series field  (( )) where   is an ordered divisible abelian group and   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  . In this paper, we study truncation integer parts of any (non-archimedean) real closed field and generalize results of Berarducci and Pitteloud. To this end, we study the canonical integer part Neg ( ) &copy ; ; ; Z of any truncation closed subfield   of  (( )), where Neg ( ) :=   \  ((  0)), and work out in detail how the general case can be reduced to the case of archimedean  . In particular, we prove that  ((  0)) &copy ; ; ; Z has (cofinally many) prime elements for any ordered divisible abelian group  . 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. Finally, we apply our results to two important classes of exponential fields: exponential algebraic power series and exponential-logarithmic power series.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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