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arXiv · 1908.06365

A Dedekind's Criterion over Valued Fields

Lhoussain El Fadil·Mhammed Boulagouaz·Abdulaziz Deajim
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Abstract

Let $(K,\nu)$ be an arbitrary-rank valued field, $R_\nu$ its valuation ring, $K(\alpha)/K$ a separable finite field extension generated over $K$ by a root of a monic irreducible polynomial $f\in R_\nu[X]$. We give necessary and sufficient conditions for $R_\nu[\alpha]$ to be integrally closed. We further characterize the integral closedness of $R_\nu[\alpha]$ based on information about the valuations on $K(\alpha)$ extending $\nu$. Our results enhance and generalize some existing results in the relevant literature. Some applications and examples are also given.

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Lhoussain El Fadil, Mhammed Boulagouaz, Abdulaziz Deajim. 2019-08-18. A Dedekind's Criterion over Valued Fields. https://arxiv.org/abs/1908.06365

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