Dedekind's criterion for the monogenicity of a number field versus Uchida's and Lüneburg's
Dedekind's criterion for the monogenicity of a number field versus Uchida's and Lüneburg's
We compare three different characterizations, due respectively to R. Dedekind, K. Uchida, and H. Lüneburg, of when, given an algebraic integer, the ring generated by it coincides with the ring of integers of its quotient field, and apply our results to some concrete 2-towers of number fields.