Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

, Volume 79, Issue 2, pp 165-187

First online:

Jacobi and Kummer’s ideal numbers

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In this article we give a modern interpretation of Kummer’s ideal numbers and show how they developed from Jacobi’s work on cyclotomy, in particular the methods for studying “Jacobi sums” which he presented in his lectures on number theory and cyclotomy in the winter semester 1836/37.


Jacobi Kummer Dedekind Ideal primes Cyclotomic fields Fermat’s last theorem Valuations Integral closure

Mathematics Subject Classification (2000)

01A55 11R18