On the real algebra of quasianalytic function germs
نویسنده
چکیده
Given a quasianalytic system Q = (Qn)n∈N of sheaves, denote by Qn the local ring of Q-analytic function germs at 0 ∈ Rn. This paper introduces the concepts of Lojasiewicz radical and geometric spectrum SpegQn ⊂ SperQn. Via the Lojasiewicz inequality, a version of the Nullstellensatz for Qn is given. We establish a quasianalytic version of the Artin–Lang property for Qn. Finally, we prove, by means of transformation to normal crossings by blowing up, that the Lojasiewicz radical £(I) of any ideal I ⊂ Qn coincides with the contraction of the real radical <(IQ̂n).
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