Capitulation in the genus fields of an abelian extension of an imaginary quadratic field

[摘要] The aim of this note is to generalize the Principal Ideal Theorem to the genus field of an abelian extension of a quadratic imaginary field k. We use the complex multiplication theory to Find explicit generators for ambiguous ideals in the genus field of some abelian extensions of k. (C) 2000 Academic Press.

[发布日期] 2000-11-01

[关键词] capitulation;genus field;ambiguous ideals.