Algebraic Element

In mathematics, if A is an associative algebra over a field K, an element a of A is called algebraic over K if some non-zero polynomial with coefficients in K vanishes when a is substituted into it; an element of A that is not algebraic over K is instead called transcendental over K. In the special case where A is itself a field extension L of K, an extension in which every element of L is algebraic over K is called an algebraic extension. The distinction generalizes the more familiar split between algebraic numbers and transcendental numbers, which is the same distinction applied to the extension of the complex numbers over the rational numbers.