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On ideals of the algebra of \(p\)-adic bounded analytic functions on a disk. (English) Zbl 1182.46059

Summary: Let \(K\) be an algebraically closed field, complete for a nontrivial ultrametric absolute value. We denote by \(A\) the \(K\)-Banach algebra of bounded analytic functions in the unit disk \(\{x\in K \mid |x|<1\}\). We study some properties of ideals of \(A\). We show that maximal ideals of infinite codimension are not of finite type and that \(A\) is not a Bézout ring.

MSC:

46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
12J25 Non-Archimedean valued fields
46J10 Banach algebras of continuous functions, function algebras
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Full Text: Euclid