M. E. Charkani, O. Lahlou, "On Dedekind's criterion and monogenicity over Dedekind rings", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 157836, 10 pages, 2003. https://doi.org/10.1155/S0161171203211534
On Dedekind's criterion and monogenicity over Dedekind rings
We give a practical criterion characterizing the monogenicity of the integral closure of a Dedekind ring , based on results on the resultant of the minimal polynomial of a primitive integral element and of its irreducible factors modulo prime ideals of . We obtain a generalization and an improvement of the Dedekind criterion (Cohen, 1996), and we give some applications in the case where is a discrete valuation ring or the ring of integers of a number field, generalizing some well-known classical results.
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