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| Main Author: | |
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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1710.01228 |
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Table of Contents:
- We give an example of a non-noetherian quasi-analytic ring constructed using a quasi-analytic Denjoy-Carleman class. If we denote by $ \mathcal{D}_n$ the ring of those $ C^\infty$ quasianalytic function germs at $0\in \mathbb{R}^n$ which are definable in a polynomially bounded o-minimal structure. We show that the system $\{ \mathcal{D}_n\,/\, n\in\mathbb{N}^*\}$ is not noetherian, i.e. there exists $m\in\mathbb{N}$, $m > 1$, such that the ring $\mathcal{D}_m$ is not noetherian.