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september 2019 Finite codimensional maximal ideals in subalgebras of ultrametric uniformly continuous functions
Monique Chicourrat, Bertin Diarra, Alain Escassut
Bull. Belg. Math. Soc. Simon Stevin 26(3): 413-420 (september 2019). DOI: 10.36045/bbms/1568685655

Abstract

Let $\rm I\!E$ be a complete ultrametric space, let $\rm I\!E$ be a perfect complete ultrametric field and let $A$ be a Banach $\rm I\!E$-algebra which is either a full $\rm I\!E$-subalgebra of the algebra of continuous functions from $\rm I\!E$ to $\rm I\!E$ owning all characteristic functions of clopens of $\rm I\!E$, or a full $\rm I\!E$-subalgebra of the algebra of uniformly continuous functions from $\rm I\!E$ to $\rm I\!E$ owning all characteristic functions of uniformly open subsets of $\rm I\!E$. We prove that all maximal ideals of finite codimension of $A$ are of codimension $1$.

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Monique Chicourrat. Bertin Diarra. Alain Escassut. "Finite codimensional maximal ideals in subalgebras of ultrametric uniformly continuous functions." Bull. Belg. Math. Soc. Simon Stevin 26 (3) 413 - 420, september 2019. https://doi.org/10.36045/bbms/1568685655

Information

Published: september 2019
First available in Project Euclid: 17 September 2019

zbMATH: 07120723
MathSciNet: MR4007606
Digital Object Identifier: 10.36045/bbms/1568685655

Subjects:
Primary: ‎46S10
Secondary: 30D35, 30G06

Rights: Copyright © 2019 The Belgian Mathematical Society

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Vol.26 • No. 3 • september 2019
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