 Dedekind realized early on that several of the notions and techniques he had introduced in algebraic number theory could be transferred to the study of algebraic functions (algebraic function fields, in later terminology), especially the set-theoretic introduction of ideals and ways of calculating with them (cf. Haffner 2014, 2015, 2017 for emphasizing the latter). This realization came to fruition in “Theorie der algebraischen Funktionen einer Veränderlichen”,  a substantive article co-written with Heinrich Weber and published in 1882. The approach in it led, among others, to a better understanding of Riemann surfaces, including a purely algebraic proof of the celebrated Riemann-Roch Theorem (Geyer 1981, Kolmogorov &amp; Yushkevich 2001, ch. 2, Stillwell 2012). As these were issues of wide interest among mathematicians, the success gave Dedekind’s approach significant legitimacy and publicity (cf. Edwards 1983, Dieudonné 1985).