On the central ideal class group of cyclotomic fields
نویسندگان
چکیده
منابع مشابه
Ideal Class Groups of Cyclotomic Number Fields I
Following Hasse’s example, various authors have been deriving divisibility properties of minus class numbers of cyclotomic fields by carefully examining the analytic class number formula. In this paper we will show how to generalize these results to CM-fields by using class field theory. Although we will only need some special cases, we have also decided to include a few results on Hasse’s unit...
متن کاملIdeal Class Groups of Cyclotomic Number Fields Ii
We first study some families of maximal real subfields of cyclotomic fields with even class number, and then explore the implications of large plus class numbers of cyclotomic fields. We also discuss capitulation of the minus part and the behaviour of p-class groups in cyclic ramified p-extensions. This is a continuation of [13]; parts I and II are independent, but will be used in part III. 6. ...
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We present a concise and self-contained definition of the ideal class group, which is useful for proving facts about zero sets of Diophantine equations, and discuss a few relevant key facts. We approach this by first assembling some preliminary definitions regarding algebraic integers, and subsequently delving into several useful results about lattices, including Minkowski’s lemma. Then, return...
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When we form a finite algebraic extension of Q, we are not guaranteed that the ring of integers, O, in our extension will be a unique factorization domain (UFD). We can obtain a measure of how far O is from being a UFD by computing the class number which is defined as the order of the ideal class group. This paper describes the ideal class group and provides examples of how to compute this grou...
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Let q be a prime power and let Fq be the nite eld with q elements. For each polynomial Q(T) in FqT ], one could use the Carlitz module to construct an abelian extension of Fq(T), called a Carlitz cyclotomic extension. Carlitz cyclotomic extensions play a fundamental role in the study of abelian extensions of Fq(T), similar to the role played by cyclotomic number elds for abelian extensions of Q...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1979
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000024879