Geodesic
Weierstrass Division in Quasianalytic Local Rings
Canadian journal of mathematics, Tome 28 (1976) no. 5, pp. 938-953

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we consider the problem of extending the Weierstrass division theorem to quasianalytic local rings of germs of functions of k real variables which properly contain the local ring of germs of analytic functions. After some background material (§ 2) and some technical preliminaries (§ 3), we show by examples that the so-called generic division theorem fails in such rings if k ≧ 1 and that the Weierstrass division theorem fails in such rings if k ≧ 2 (§ 4). 
Childress, C. L. Weierstrass Division in Quasianalytic Local Rings. Canadian journal of mathematics, Tome 28 (1976) no. 5, pp. 938-953. doi: 10.4153/CJM-1976-091-7
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