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Luka Thaler
Luka Thaler
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Since I found the answer to my question I will write it here, hoping that it will be helpful to someone else.

Answer: The ring of global real analytic functions on a compact real analytic Stein manifold is noetherian due to Theorem I.9. [J.Frisch.: Points de platitude d'un morphisme d'espaces analytiques complexes. Invent. Math., 4:118-138, 1967.], see also last paragraph in [J. M. Ruiz. On Hilbert's 17th problem and real Nullstellensatz for global analytic functions. Math. Z., 190(3):447-454, 1985]

Since I found the answer to my question I will write it here, hoping that it will be helpful to someone else.

Answer: The ring of global real analytic functions on a compact real analytic manifold is noetherian due to Theorem I.9. [J.Frisch.: Points de platitude d'un morphisme d'espaces analytiques complexes. Invent. Math., 4:118-138, 1967.], see also last paragraph in [J. M. Ruiz. On Hilbert's 17th problem and real Nullstellensatz for global analytic functions. Math. Z., 190(3):447-454, 1985]

Since I found the answer to my question I will write it here, hoping that it will be helpful to someone else.

Answer: The ring of global real analytic functions on a compact real analytic Stein manifold is noetherian due to Theorem I.9. [J.Frisch.: Points de platitude d'un morphisme d'espaces analytiques complexes. Invent. Math., 4:118-138, 1967.], see also last paragraph in [J. M. Ruiz. On Hilbert's 17th problem and real Nullstellensatz for global analytic functions. Math. Z., 190(3):447-454, 1985]

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Luka Thaler
Luka Thaler
  • 589
  • 5
  • 15

Since I found the answer to maymy question I will write it here, hoping that it will be helpful to someone else.

Answer: The ring of global real analytic functions on a compact real analytic manifold is noetherian due to Theorem I.9. [J.Frisch.: Points de platitude d'un morphisme d'espaces analytiques complexes. Invent. Math., 4:118-138, 1967.], see also last paragraph in [J. M. Ruiz. On Hilbert's 17th problem and real Nullstellensatz for global analytic functions. Math. Z., 190(3):447-454, 1985]

Since I found the answer to may question I will write it here, hoping that it will be helpful to someone else.

Answer: The ring of global real analytic functions on a compact real analytic manifold is noetherian due to Theorem I.9. [J.Frisch.: Points de platitude d'un morphisme d'espaces analytiques complexes. Invent. Math., 4:118-138, 1967.], see also last paragraph in [J. M. Ruiz. On Hilbert's 17th problem and real Nullstellensatz for global analytic functions. Math. Z., 190(3):447-454, 1985]

Since I found the answer to my question I will write it here, hoping that it will be helpful to someone else.

Answer: The ring of global real analytic functions on a compact real analytic manifold is noetherian due to Theorem I.9. [J.Frisch.: Points de platitude d'un morphisme d'espaces analytiques complexes. Invent. Math., 4:118-138, 1967.], see also last paragraph in [J. M. Ruiz. On Hilbert's 17th problem and real Nullstellensatz for global analytic functions. Math. Z., 190(3):447-454, 1985]

Source Link
Luka Thaler
Luka Thaler
  • 589
  • 5
  • 15

Since I found the answer to may question I will write it here, hoping that it will be helpful to someone else.

Answer: The ring of global real analytic functions on a compact real analytic manifold is noetherian due to Theorem I.9. [J.Frisch.: Points de platitude d'un morphisme d'espaces analytiques complexes. Invent. Math., 4:118-138, 1967.], see also last paragraph in [J. M. Ruiz. On Hilbert's 17th problem and real Nullstellensatz for global analytic functions. Math. Z., 190(3):447-454, 1985]