- Tytuł:
- Noethérianité de certaines algèbres de fonctions analytiques et applications
- Autorzy:
-
Elkhadiri, Abdelhafed
Hlal, Mouttaki - Powiązania:
- https://bibliotekanauki.pl/articles/1207892.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Nash functions
regular rings
analytic algebra
subanalytic sets - Opis:
-
Let $M ⊂ ℝ^{n}$ be a real-analytic submanifold and H(M) the algebra of real analytic functions on M. If K ⊂ M is a compact subset we consider $S_{K}={f ∈ H(M)| f(x) ≠ 0 \ \text{for all} \ x ∈ K}$; $S_{K}$ is a multiplicative subset of $H(M)$. Let $S_{K}^{-1}H(M)$ be the localization of H(M) with respect to $S_{K}$. In this paper we prove, first, that $S_{K}^{-1}H(M)$ is a regular ring (hence noetherian) and use this result in two situations:
1) For each open subset $Ω ⊂ ℝ^{n}$, we denote by O(Ω) the subalgebra of H(Ω) defined as follows: f ∈ O(Ω) if and only if for all x ∈ Ω, the germ of f at x, $f_{x}$, is algebraic on $H(ℝ^{n})$. We prove that if Ω is a bounded subanalytic subset, then O(Ω) is a regular ring (hence noetherian).
2) Let $M ⊂ ℝ^{n}$ be a Nash submanifold and N(M) the ring of Nash functions on M; we have an injection N(M) → H(M). In [2] it was proved that every prime ideal p of N(M) generates a prime ideal of analytic functions pH(M) if M or V(p) is compact. We use our Theorem 1 to give another proof in the situation where V(p) is compact. Finally we show that this result holds in some particular situation where M and V(p) are not assumed to be compact. - Źródło:
-
Annales Polonici Mathematici; 2000, 75, 3; 247-256
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł