Dedekind's "different": sources, definition, original name

Question

I am interested in getting the original information regarding Dedekind's idea of the "different" (regarding ideals). Particularly, I am interested in:

1- Knowing the original German name he used for it. I think it was "diskriminant", but I am not sure. 2-Getting his original definition (It would be great if the page could be scanned and bibliographic reference could be given).

Thanks."

Answer 1

See :

• Nicolas Bourbaki, Elements of the History of Mathematics, (French ed, 1984), page 102 :

in 1882, Dedekind completes the theory [of ideals] by introducing the different, which gives him a new definition of the discriminant and allows him to specify the exponents of the prime ideal factors in the decomposition of the latter.

In the German text of : Richard Dedekind, Über die Discriminanten endlicher Körper, 1882, Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen 29 (2): 1–56, see page 1 for : "Grundzahl oder Discriminante" and page 38 for : "Grundideal des Körpers".