Naslov
Exponential Integer Parts of Non-archimedean Exponential Fields

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

Izvornik
L'Equipe de Logique Mathématique - prepublications 76 (2004) (1) 1-18

Vrsta, podvrsta
Ostale vrste radova, ostali članci/prilozi

Godina
2004

Ključne riječi
truncation; integer part; irreducible; exponential field

Sažetak
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 con- centrated on the case of archimedean G. 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 (F) \oplus Z of any truncation closed subfield F of k((G)), where Neg (F) := F \ k((G<0)), and work out in detail how the general case can be reduced to the case of archimedean G. 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 expo- nential 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 serie

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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