Quadratic field

Real quadratic field

A real quadratic field is a quadratic field where , alg and hence signature .

Properties

1. The group of units is for the fundamental unit , uniquely determined by .¹ See Fundamental unit of a real quadratic field.

Proof

^P1 easily follows from Dirichlet’s unit theorem, since we have

as required.

Examples

• Rationals adjoin sqrt(223).

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Footnotes

1. To find a fundamental unit, show that if for , then . ↩