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The Genus Field and Genus Number in Algebraic Number Fields

Published online by Cambridge University Press:  22 January 2016

Yoshiomi Furuta
Yoshiomi Furuta*
Affiliation:
Mathematical Institute, Kanazawa University
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Let k be an algebraic number field and K be its normal extension of finite degree. Then the genus field K* of K over k is defined as the maximal unramified extension of K which is obtained from K by composing an abelian extension over k2). We call the degree (K*: K) the genus number of K over k.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 29 , March 1967 , pp. 281 - 285
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1967

References

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