On the capitulation in the genus field of an abelian extension of an imaginary quadratic field (Q1590282)
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scientific article; zbMATH DE number 1547376
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the capitulation in the genus field of an abelian extension of an imaginary quadratic field |
scientific article; zbMATH DE number 1547376 |
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On the capitulation in the genus field of an abelian extension of an imaginary quadratic field (English)
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1 January 2001
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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 \(k\).
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