Quadratic field

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Revision as of 04:47, 7 December 2008 by imported>Richard Pinch (skeleton section headings; supplied reference Stewart+Tall)
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In mathematics, a quadratic field is a field which is an extension of its prime field of degree two.

In the case when the prime field is finite, so is the quadratic field, and we refer to the article on finite fields. In this article we treat quadratic extensions of the field Q of rational numbers.

In characteristic zero, every quadratic equation is soluble by taking one square root, so a quadratic field is of the form for a non-zero non-square rational number d. Multiplying by a square integer, we may assume that d is in fact a square-free integer.

Ring of integers

Unit group

Class group

Splitting of primes

References