Pregled bibliografske jedinice broj: 278988
Primes and Irreducibles in Truncation Integer Parts of Real Closed Fields
Primes and Irreducibles in Truncation Integer Parts of Real Closed Fields // Logic in Tehran: proceedings of the Workshop and Conference on Logic, Algebra, and Arithmetic / Enayat, Ali ; Kalantari, Iraj ; Moniri. Mojtaba (ur.).
Wellesley (MA): Association for Symbolic Logic, A K Peters Ltd, , (2006), 42-64 ;, 2006. str. 42-64 (poster, međunarodna recenzija, cjeloviti rad (in extenso), znanstveni)
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Naslov
Primes and Irreducibles in Truncation Integer Parts of Real Closed Fields
Autori
Biljaković, 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 the Workshop and Conference on Logic, Algebra, and Arithmetic
/ Enayat, Ali ; Kalantari, Iraj ; Moniri. Mojtaba - Wellesley (MA) : Association for Symbolic Logic, A K Peters Ltd, , (2006), 42-64 ;, 2006, 42-64
ISBN
978-1-56881-296-0
Skup
Logic in Tehran: the Workshop and Conference on Logic, Algebra, and Arithmetic
Mjesto i datum
Teheran, Iran, 18.10.2003. - 22.10.2003
Vrsta sudjelovanja
Poster
Vrsta recenzije
Međunarodna recenzija
Ključne riječi
Prime; irreducible; truncation; integer part; real closed field; generalized power series; exponential integer part
Sažetak
Berarducci (2000) studied irreducible elements of the ring k((G<0))⊕ 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) ⊕ 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)) ⊕ 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 series.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Projekti:
0120047
Ustanove:
Fakultet strojarstva i brodogradnje, Zagreb,
Agronomski fakultet, Zagreb
Profili:
Darko Biljaković
(autor)
