## Weierstrass division theorem in quasianalytic local rings

### Volume 185 / 2008

Studia Mathematica 185 (2008), 83-86
MSC: Primary 26E10, 32B05; Secondary 58C10.
DOI: 10.4064/sm185-1-5

#### Abstract

The main result of this paper is the following: if the Weierstrass division theorem is valid in a quasianalytic differentiable system, then this system is contained in the system of analytic germs. This result has already been known for particular examples, such as the quasianalytic Denjoy–Carleman classes.