Division dans l'anneau des séries formelles
à croissance contrôlée.
Applications
Studia Mathematica, Tome 144 (2001) no. 1, pp. 63-93
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $A.$
Mots-clés :
consider subrings ring formal power series defined growth conditions coefficients instance gevrey conditions prove weierstrass hironaka division theorem subrings moreover given ideal mathcal series prove existence unique remainder modulo mathcal consequence get proof noetherianity
Affiliations des auteurs :
Augustin Mouze 1
@article{10_4064_sm144_1_3,
author = {Augustin Mouze},
title = {Division dans l'anneau des s\'eries formelles
\`a croissance {contr\^ol\'ee.
Applications}},
journal = {Studia Mathematica},
pages = {63--93},
publisher = {mathdoc},
volume = {144},
number = {1},
year = {2001},
doi = {10.4064/sm144-1-3},
language = {fr},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm144-1-3/}
}
TY - JOUR AU - Augustin Mouze TI - Division dans l'anneau des séries formelles à croissance contrôlée. Applications JO - Studia Mathematica PY - 2001 SP - 63 EP - 93 VL - 144 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm144-1-3/ DO - 10.4064/sm144-1-3 LA - fr ID - 10_4064_sm144_1_3 ER -
Augustin Mouze. Division dans l'anneau des séries formelles à croissance contrôlée. Applications. Studia Mathematica, Tome 144 (2001) no. 1, pp. 63-93. doi: 10.4064/sm144-1-3
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