Abstract:Let R be a Dedekind ring, K its quotient field, and L = K(α) a finite field extension of K defined by a monic irreducible polynomial f (x) ∈ R[x]. We give an easy version of Dedekind's criterion which computationally improves those versions know in the literature. We further use this result to give a sufficient condition for the integral closedness of R[α] when f (x) = x n − a. In case R is a ring of integers of a number field, we give yet sufficient and necessary conditions for this to hold, generalizing and … Show more
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