Division dans l'anneau des séries formelles à croissance contrôlée. Applications
Volume 144 / 2001
Studia Mathematica 144 (2001), 63-93
MSC: 13F25, 13J15, 16P40, 32A05.
DOI: 10.4064/sm144-1-3
Abstract
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 ${\mathcal I}$ of $A$ and a series $f$ in $A$ we prove the existence in $A$ of a unique remainder $r$ modulo ${\mathcal I}.$ As a consequence, we get a new proof of the noetherianity of $A.$
