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.
@article{bwmeta1.element.bwnjournal-article-bcpv44i1p277bwm,
author = {Zurro, Maria-Angeles},
title = {On the rings of formal solutions of polynomial differential equations},
journal = {Banach Center Publications},
volume = {43},
year = {1998},
pages = {277-292},
zbl = {0953.32004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv44i1p277bwm}
}
Zurro, Maria-Angeles. On the rings of formal solutions of polynomial differential equations. Banach Center Publications, Tome 43 (1998) pp. 277-292. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv44i1p277bwm/
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