Quadratic field

Real quadratic field

A real quadratic field is a quadratic field where , #m/def/num/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

#state/tidy | #lang/en | #SemBr

Footnotes

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