Division dans l'anneau des séries formelles à croissance contrôlée. Applications

• Autorzy: Augustin Mouze
• Języki publikacji: FR EN

Abstrakty

EN

We consider subrings A of the ring of formal power series. They are defined by growth conditions on coefficients such as, for instance, Gevrey conditions. We prove a Weierstrass-Hironaka division theorem for such subrings. Moreover, given an ideal ℐ of A and a series f in A we prove the existence in A of a unique remainder r modulo ℐ. As a consequence, we get a new proof of the noetherianity of A.

Kategorie tematyczne

• 13J15: Henselian rings
• 13F25: Formal power series rings
• 32A05: Power series, series of functions
• 16P40: Noetherian rings and modules

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 144
• Numer: 1
• Strony: 63-93

Daty

wydano

2001

Twórcy

autor

Augustin Mouze

• CNRS-UMR 8524, Mathématiques, bâtiment M2, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex, France

Identyfikatory

DOI

10.4064/sm144-1-3