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.
Publié le : 2007-12-14
Classification:
bounded analytic functions,
ideals of infinite type,
12J25,
46S10
@article{1197908900,
author = {Escassut, Alain and Ma\"\i netti, Nicolas},
title = {On Ideals of the Algebra of $p$-adic Bounded Analytic Functions on a Disk},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {13},
number = {5},
year = {2007},
pages = { 871-876},
language = {en},
url = {http://dml.mathdoc.fr/item/1197908900}
}
Escassut, Alain; Maïnetti, Nicolas. On Ideals of the Algebra of $p$-adic Bounded Analytic Functions on a Disk. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp. 871-876. http://gdmltest.u-ga.fr/item/1197908900/