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Class Number and Ramification in Number Fields

Published online by Cambridge University Press:  22 January 2016

Armand Brumer  and
Michael Rosen
Armand Brumer
Affiliation:
Boston College, Brown University
Michael Rosen
Affiliation:
Boston College, Brown University
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In the ring Ok of algebraic integers of a number field K the group Ik of ideals of Ok modulo the subgroup Pk of principal ideals is a finite abelian group of order hk , the class number of K. The determination of this number is an outstanding problem of algebraic number theory.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 23 , December 1963 , pp. 97 - 101
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1963

References

[1] Leopoldt, H. Sur Geschlertertheorie in abelschen Zahlkörpern, Math. Nach. Vol. 9 (1953).Google Scholar
[2] Serre, J. P. Cohomologie des groupes et applicatione arithmetiques, Collège de France 1958.Google Scholar
[3] Chevalley, Cl. Class field theory, Notes at Nagoya University 1954.Google Scholar
[4] Artin-Tate Class field theory, Notes by Lang, S., Harvard 1956.Google Scholar