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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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| _version_ | 1866913633582186496 |
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| author | Elkhadiri, Abdelhafed |
| author_facet | Elkhadiri, Abdelhafed |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1710_01228 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Some non noetherian $C^\infty$ quasianalytic local rings Elkhadiri, Abdelhafed Algebraic Geometry 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. |
| title | Some non noetherian $C^\infty$ quasianalytic local rings |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1710.01228 |