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On the Units of Algebraic Number Fields

✍ Scribed by I. Yamaguchi; H. Takeuchi

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
99 KB
Volume
49
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let (K) be an algebraic number field and (k) be a proper subfield of (K). Then we have the relations between the relative degree ([K: k]) and the increase of the rank of the unit groups. Especially, in the case of (m) th cyclotomic field (Q\left(\zeta_{m}\right)), we determine the number (m) such that the increase of the rank of the unit groups is equal to the number of the imaginary conjugates of the proper subfield. C 1994 Academic Press, Inc.

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