Bulletin of the Belgian Mathematical Society - Simon Stevin

On Ideals of the Algebra of $p$-adic Bounded Analytic Functions on a Disk

Alain Escassut and Nicolas Maïnetti

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Abstract

Let $K$ be an algebraically closed field, complete for a non-trivial ultrametric absolute value. We denote by $A$ the $K$- Banach algebra of bounded analytic functions in the unit disk $\{x\in K \mid \vert x\vert<1\}$. 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 Bezout ring.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 5 (2007), 871-876.

Dates
First available in Project Euclid: 17 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1197908900

Digital Object Identifier
doi:10.36045/bbms/1197908900

Mathematical Reviews number (MathSciNet)
MR2378994

Zentralblatt MATH identifier
1182.46059

Subjects
Primary: 12J25: Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10] 46S10: Functional analysis over fields other than $R$ or $C$ or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]

Keywords
bounded analytic functions ideals of infinite type

Citation

Escassut, Alain; Maïnetti, Nicolas. On Ideals of the Algebra of $p$-adic Bounded Analytic Functions on a Disk. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 5, 871--876. doi:10.36045/bbms/1197908900. https://projecteuclid.org/euclid.bbms/1197908900


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