We give a practical criterion characterizing the monogenicity of the integral closure of a Dedekind ring R, based on results on the resultant Res(P , P i ) of the minimal polynomial P of a primitive integral element and of its irreducible factors P i modulo prime ideals of R. We obtain a generalization and an improvement of the Dedekind criterion (Cohen, 1996) and we give some applications in the case where R is a discrete valuation ring or the ring of integers of a number field, generalizing some well-known classical results.Mathematics Subject Classification: 11Y40, 13A18, 13F30.
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