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?
2026-03-25 13:42:07.1774446127
Reference for Dedekind's Example of a Non-monogenic Field
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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.