The Genus Field and Genus Number in Algebraic Number Fields
- 1 March 1967
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 29, 281-285
- https://doi.org/10.1017/s0027763000024387
Abstract
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 k 2). We call the degree (K*: K) the genus number of K over k.Keywords
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