On the rings of formal solutions of polynomial differential equations

Volume 44 / 1998

Maria-Angeles Zurro Banach Center Publications 44 (1998), 277-292 DOI: 10.4064/-44-1-277-292

Abstract

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.

Authors

  • Maria-Angeles Zurro

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