Corollary 2.53 . [00IT]

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Corollary 2.53.

Any strict affinoid algebra is Noetherian. All of its ideals are closed ([BGR, Proposition 6.1.1.3], [FvdP, Theorem 3.2.1]). Any affinoid algebra is Noetherian. All of its ideals are closed ([Ber, Propositon 2.1.3]).