Dedekind's work was quickly accepted, partly because of the clarity with which he presented his ideas and partly since Heinrich Weber lectured to Hilbert on these topics at the University of Königsberg. Dedekind's notion of ideal was taken up and extended by Hilbert and then later by Emmy Noether .
Dedekind ng trabaho ay mabilis na tinanggap, bahagya dahil sa ang liwanag na kung saan ipinapahayag niya ang kanyang mga ideya at bahagyang dahil Heinrich Weber lectured sa Hilbert sa mga paksang ito sa University of Königsberg. Dedekind ng kuru-kuro ng ideal na kinuha up at extended sa pamamagitan ng Hilbert at pagkatapos ay mamaya sa pamamagitan ng Emmy Noether.