On the rings of formal solutions of polynomial differential equations
Volume 44 / 1998
Banach Center Publications 44 (1998), 277-292 DOI: 10.4064/-44-1-277-292
The paper establishes the basic algebraic theory for the Gevrey rings. We prove the Hensel lemma, the Artin approximation theorem and the Weierstrass-Hironaka division theorem for them. We introduce a family of norms and we look at them as a family of analytic functions defined on some semialgebraic sets. This allows us to study the analytic and algebraic properties of this rings.