# On a Theorem of Dedekind

@inproceedings{Deajim2021OnAT, title={On a Theorem of Dedekind}, author={Abdulaziz Deajim and Lhoussain El Fadil and Ahmed Najim}, year={2021} }

Let (K, ν) be an arbitrary valued field with valuation ring Rν and L = K(α), where α is a root of a monic irreducible polynomial f ∈ Rν [x]. In this paper, we characterize the integral closedness of Rν [α] in such a way that extend Dedekind’s criterion. Without the assumption of separability of the extension L/K, we show that Dedekind’s theorem and its converse hold.

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