Division dans l'anneau des séries formelles à croissance contrôlée. Applications

Augustin Mouze

Studia Mathematica (2001)

  • Volume: 144, Issue: 1, page 63-93
  • ISSN: 0039-3223

Abstract

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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 ℐ of A and a series f in A we prove the existence in A of a unique remainder r modulo ℐ. As a consequence, we get a new proof of the noetherianity of A.

How to cite

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Augustin Mouze. "Division dans l'anneau des séries formelles à croissance contrôlée. Applications." Studia Mathematica 144.1 (2001): 63-93. <http://eudml.org/doc/284703>.

@article{AugustinMouze2001,
author = {Augustin Mouze},
journal = {Studia Mathematica},
keywords = {formal power series; growth conditions on coefficients; Gevrey conditions; Weierstrass-Hironaka division theorem; Noetherianness},
language = {fre},
number = {1},
pages = {63-93},
title = {Division dans l'anneau des séries formelles à croissance contrôlée. Applications},
url = {http://eudml.org/doc/284703},
volume = {144},
year = {2001},
}

TY - JOUR
AU - Augustin Mouze
TI - Division dans l'anneau des séries formelles à croissance contrôlée. Applications
JO - Studia Mathematica
PY - 2001
VL - 144
IS - 1
SP - 63
EP - 93
LA - fre
KW - formal power series; growth conditions on coefficients; Gevrey conditions; Weierstrass-Hironaka division theorem; Noetherianness
UR - http://eudml.org/doc/284703
ER -

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