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[parent] imaginary quadratic field (Definition)

A quadratic number field $\mathbb{Q}(\sqrt{d})$ where $d$ is a negative squarefree integer, is called a imaginary quadratic field.

The name may be thought to describe the fact that such a quadratic field contains ``imaginary numbers'' (in the sense `non-real complex numbers').

Other quadratic fields are real quadratic fields.




"imaginary quadratic field" is owned by pahio.
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See Also: imaginary, units of quadratic fields, quadratic imaginary norm-Euclidean number fields, list of all imaginary quadratic extensions whose ring of integers is a PID

Other names:  quadratic imaginary field, imaginary quadratic number field, quadratic imaginary number field, imaginary quadratic extension
Also defines:  real quadratic field

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Attachments:
class numbers of imaginary quadratic fields (Data Structure) by pahio
lemma for imaginary quadratic fields (Theorem) by pahio
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Cross-references: complex numbers, quadratic field, integer, squarefree, negative, quadratic number field
There are 25 references to this entry.

This is version 5 of imaginary quadratic field, born on 2008-04-05, modified 2008-10-27.
Object id is 10480, canonical name is ImaginaryQuadraticField.
Accessed 3159 times total.

Classification:
AMS MSC11R04 (Number theory :: Algebraic number theory: global fields :: Algebraic numbers; rings of algebraic integers)
 11R11 (Number theory :: Algebraic number theory: global fields :: Quadratic extensions)

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