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Algebraic Number

Basic definition

An algebraic number is a number that is the root of some polynomial with integer coefficients. Algebraic numbers can be real or complex and need not be rational.

Detailed definition

If r is a root of a nonzero polynomial equation a_n x^n + a_(n - 1) x^(n - 1) + ... + a_1 x + a_0 = 0, where the a_is are integers (or equivalently, rational numbers) and r satisfies no similar equation of degree <n, then r is said to be an algebraic number of degree n. A number that is not algebraic is said to be transcendental. If r is an algebraic number and a_n = 1, then it is called an algebraic integer.

Related terms

algebraic integer | algebraic number minimal polynomial | algebraic number theory | algebraic period | Euclidean number | Hermite-Lindemann theorem | number field | Q^_ | radical integer | transcendental number

Educational grade level

college level

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