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.
@article{bwmeta1.element.bwnjournal-article-doi-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},
volume = {147},
year = {2001},
pages = {63-93},
zbl = {0972.13016},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm144-1-3}
}
Augustin Mouze. Division dans l'anneau des séries formelles à croissance contrôlée. Applications. Studia Mathematica, Tome 147 (2001) pp. 63-93. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm144-1-3/