scholarly journals Triviality in ideal class groups of Iwasawa-theoretical abelian number fields

2005 ◽  
Vol 57 (3) ◽  
pp. 827-857 ◽  
Author(s):  
Kuniaki HORIE
Keyword(s):  
Number Fields ◽  
Ideal Class ◽  
Class Groups ◽  
Ideal Class Groups

scholarly journals A Note on Ideal Class Groups

1966 ◽  
Vol 27 (1) ◽  
pp. 239-247 ◽  
Author(s):  
Kenkichi Iwasawa
Keyword(s):  
Class Group ◽  
Cyclotomic Field ◽  
Theoretical Method ◽  
Number Fields ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Class Groups ◽  
Algebraic Number Fields ◽  
Ideal Class Groups ◽  
The Ideal

In the first part of the present paper, we shall make some simple observations on the ideal class groups of algebraic number fields, following the group-theoretical method of Tschebotarew. The applications on cyclotomic fields (Theorems 5, 6) may be of some interest. In the last section, we shall give a proof to a theorem of Kummer on the ideal class group of a cyclotomic field.

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