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On Analytic Functions in an Ordered Field with an Infinite Rank Valuation

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Abstract

Let \(K\) be the scalar field of the first orthomodular (or Form Hilbert) space, described by H. Keller in \(1980\). It has a non-Archimedean order, an infinite rank valuation compatible with the order as well as an explicitly defined ultrametric, all of which induce the same topology on the valued field. We study analytic functions defined on valued field \(K\), and we will establish an invertibility local Theorem for these functions as an application of Banach fixed point Theorem on a particular complete metric space.

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References

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Funding

The author was partially supported by Proyecto PR18152 Dirección de Investigación y Desarrollo, Universidad de La Serena.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de La Serena, Avenida Cisternas 1200, La Serena, Chile

    H. M. Moreno

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  1. H. M. Moreno
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Correspondence to H. M. Moreno.

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Moreno, H.M. On Analytic Functions in an Ordered Field with an Infinite Rank Valuation. P-Adic Num Ultrametr Anal Appl 12, 310–321 (2020). https://doi.org/10.1134/S2070046620040056

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  • DOI: https://doi.org/10.1134/S2070046620040056

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