Corpus ID: 235417459

On a Theorem of Dedekind

@inproceedings{Deajim2021OnAT,
  title={On a Theorem of Dedekind},
  author={A. Deajim and L. E. Fadil and A. 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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