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Noethérianité de certaines algèbres de fonctions analytiques et applications

Abdelhafed Elkhadiri, Mouttaki Hlal (2000)

Annales Polonici Mathematici

Let M 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 f o r a l l 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 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...

Note on the degree of Cº-sufficiency of plane curves.

Antonio F. Costa (1989)

Publicacions Matemàtiques

Let f be a germ of plane curve, we define the δ-degree of sufficiency of f to be the smallest integer r such that for anuy germ g such that j(r) f = j(r) g then there is a set of disjoint annuli in S3 whose boundaries consist of a component of the link of f and a component of the link of g. We establish a formula for the δ-degree of sufficiency in terms of link invariants of plane curves singularities and, as a consequence of this formula, we obtain that the δ-degree of sufficiency is equal to the...

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