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Article Dans Une Revue Southeast Asian Bulletin of Mathematics Année : 2015

Survey on Bezout rings of p-adic analytic functions

Bertin Diarra
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Alain Escassut
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Résumé

Let K be a complete ultrametric algebraically closed field and let A(K) (resp. A(D)) be the K-algebra of analytic functions in K (resp. inside an open disk D). Following results in a paper by M. Lazard, we show that these algebras are Bezout rings, a property that is not showed in that paper. Moreover, the main results leading to the Bezout property is based upon a Mittag-Leffler theorem for meromorphic functions which is not proven in Lazard's paper. Furthermore, that Mittag-Leffler theorem (which is different from Krasner's Mittag-Leffler theorem for analytic elements) lets us find a shorter proof to show that the meromorphic functions admitting primitives are those whose residues are null. .
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Dates et versions

hal-01913280 , version 1 (06-11-2018)

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  • HAL Id : hal-01913280 , version 1

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Bertin Diarra, Alain Escassut. Survey on Bezout rings of p-adic analytic functions. Southeast Asian Bulletin of Mathematics, 2015. ⟨hal-01913280⟩
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