The Genus Field and Genus Number in Algebraic Number Fields
1967 ◽
Vol 29
◽
pp. 281-285
◽
Keyword(s):
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.
1987 ◽
Vol 107
◽
pp. 135-146
◽
1961 ◽
Vol 19
◽
pp. 169-187
◽
Keyword(s):
Keyword(s):
Keyword(s):
2012 ◽
Vol 11
(05)
◽
pp. 1250087
◽
1957 ◽
Vol 12
◽
pp. 177-189
◽
Keyword(s):
Keyword(s):
2019 ◽
Vol 15
(02)
◽
pp. 353-360
1984 ◽
Vol 93
◽
pp. 133-148
◽