On Dedekind's criterion and monogenicity over Dedekind rings

M. E. Charkani and O. Lahlou

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-10

Abstract:

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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:157836

DOI: 10.1155/S0161171203211534

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