%0 Journal Article
%T On Dedekind's criterion and monogenicity over Dedekind rings
%A M. E. Charkani
%A O. Lahlou
%J International Journal of Mathematics and Mathematical Sciences
%D 2003
%I Hindawi Publishing Corporation
%R 10.1155/s0161171203211534
%X 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,pi) of the minimal polynomial p of a primitive integral element and of its irreducible factors pi 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.
%U http://www.hindawi.com/journals/ijmms/2003/157836/abs/