A quadratic field, denoted Q(sqrt(D)), is the set of numbers of the form a + b sqrt(D), where a,b are rational numbers.

A quadratic field is denoted Q(sqrt(D))

Integers of a quadratic field are numbers of the form

r + s sqrt(D), if D≡2,3 (mod 4), or
r + s (1/2)(-1 + sqrt(D)), if D≡1 (mod 4),

where r, s are integers.

Gaussian integers are integers of the imaginary quadratic field Q(sqrt(-1))

Eisenstein integers are integers of the imaginary quadratic field Q(sqrt(-3))

 . . . . . .

Internet references

Wikipedia: 

Mathworld: Quadratic Field

Fact archive: Quadratic field, and Heegner number - an imaginary quadratic field with class number 1 (See Ideal class group).

Related pages in this website

Complex number

Eisenstein integer

Gaussian integer

The webmaster and author of this Math Help site is Graeme McRae.