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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.
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 -