PlanetMath: imaginary quadratic field

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imaginary quadratic field

(Definition)

A quadratic number field $\mathbb{Q}(\sqrt{d})$ , where 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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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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Cross-references: complex numbers, quadratic field, integer, squarefree, negative, quadratic number field
There are 22 references to this entry.

This is version 4 of imaginary quadratic field, born on 2008-04-05, modified 2008-04-06.
Object id is 10480, canonical name is ImaginaryQuadraticField.
Accessed 881 times total.

Classification:

AMS MSC:	11R04 (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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