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Denis Serre
Denis Serre
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Do real analytic functions on $\mathbb{C}\mathbb{P}^n$ form a Noetherian ring?

Question: Is the ring of real-analytic functions on $\mathbb{C}\mathbb{P}^n$ (real valued) a Noetherian ring?

References or counterexamples are welcome.

I know that the ring of germs of holomorphic functions on $\mathbb{C}^n$ is Noetherian, but the ring of holomorphic functions on $\mathbb{C}^n$ is not  ! I also know how to verify that the ring of polynomials is Noetherian.

Do real analytic functions on $\mathbb{C}\mathbb{P}^n$ form a Noetherian ring

Question: Is the ring of real-analytic functions on $\mathbb{C}\mathbb{P}^n$ (real valued) a Noetherian ring?

References or counterexamples are welcome.

I know that the ring of germs of holomorphic functions on $\mathbb{C}^n$ is Noetherian, but the ring of holomorphic functions on $\mathbb{C}^n$ is not! I also know how to verify that the ring of polynomials is Noetherian.

Do real analytic functions on $\mathbb{C}\mathbb{P}^n$ form a Noetherian ring?

Question: Is the ring of real-analytic functions on $\mathbb{C}\mathbb{P}^n$ (real valued) a Noetherian ring?

References or counterexamples are welcome.

I know that the ring of germs of holomorphic functions on $\mathbb{C}^n$ is Noetherian, but the ring of holomorphic functions on $\mathbb{C}^n$ is not  ! I also know how to verify that the ring of polynomials is Noetherian.

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Luka Thaler
Luka Thaler
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Do real analytic functions on $\mathbb{C}\mathbb{P}^n$ form a Noetherian ring

Question: Is the ring of real-analytic functions on $\mathbb{C}\mathbb{P}^n$ (real valued) a Noetherian ring?

References or counterexamples are welcome.

I know that the ring of germs of holomorphic functions on $\mathbb{C}^n$ is Noetherian, but the ring of holomorphic functions on $\mathbb{C}^n$ is not! I also know how to verify that the ring of polynomials is Noetherian.