Jacobi and Kummer’s ideal numbers


DOI: 10.1007/s12188-009-0020-5

Cite this article as:
Lemmermeyer, F. Abh. Math. Semin. Univ. Hambg. (2009) 79: 165. doi:10.1007/s12188-009-0020-5


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 

Copyright information

© Mathematisches Seminar der Universität Hamburg and Springer 2009

Authors and Affiliations

  1. 1.JagstzellGermany

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