Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Nash functions

Sortuj według:

Ogranicz wyniki do:

Noethérianité de certaines algèbres de fonctions analytiques et applications

100%

Elkhadiri A., Hlal M.

Annales Polonici Mathematici

2000

tom 75

nr 3

247-256

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 $S_{K}={f ∈ H(M)| f(x) ≠ 0 for all x ∈ K}$; $S_{K}$ 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.

On a universal axiomatization of the real closed fields

100%

Nowak K.

Annales Polonici Mathematici

1996-1997

tom 65

nr 1

95-103

This paper presents a natural axiomatization of the real closed fields. It is universal and admits quantifier elimination.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Elkhadiri A.

1 Hlal M.

1 Nowak K.

1 2000

1 1996

Wyniki wyszukiwania

Noethérianité de certaines algèbres de fonctions analytiques et applications

On a universal axiomatization of the real closed fields