Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

, Volume 79, Issue 2, pp 165–187

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.


JacobiKummerDedekindIdeal primesCyclotomic fieldsFermat’s last theoremValuationsIntegral closure

Mathematics Subject Classification (2000)


Copyright information

© Mathematisches Seminar der Universität Hamburg and Springer 2009

Authors and Affiliations

  1. 1.JagstzellGermany