Reference for Dedekind's Example of a Non-monogenic Field An oft quoted fact is that Dedekind discovered that adjoining a root of $x^3-x^2-2x-8$ to $\mathbb{Q}$ yields a number field that is not monogenic. Does anyone...--prophetes.ai

Reference for Dedekind's Example of a Non-monogenic Field An oft quoted fact is that Dedekind discovered that adjoining a root of $x^3-x^2-2x-8$ to $\mathbb{Q}$ yields a number field that is not monogenic. Does anyone know exactly where Dedekind writes this? In other words, does anyone have the citation for this?

It can be found e.g. in his announcement of the second edition of Dirichlet's Lectures in Number Theory (Gött. gelehrte Anzeigen 1871, 1481--1494; see Dedekind Werke, vol III, p. 406). He published the details in _Über den Zusammenhang zwischen der Theorie der Ideale und der Theorie der höheren Kongruenzen_ , Gött. Abhandlungen 1878, 1--23; Werke II, 202-223; see in particularp. 225.