Abstract
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).
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