Division dans l'anneau des séries formelles à croissance contrôlée. Applications
We consider subringsA of the ring of formal power series. They are dened by growth conditions on coecien ts such as, for instance, Gevrey conditions. We prove a Weierstrass{Hironaka division theorem for such subrings. Moreover, given an idealI of A and a series f in A we prove the existence in A of a unique remainder r moduloI: As a consequence, we get a new proof of the noetherianity of A: