Algebraic element

In mathematics, if A is an associative algebra over K, then an element a of A is an algebraic element over K, or just algebraic over K, if there exists some non-zero polynomial ${\displaystyle g(x)\in K[x]}$ with coefficients in K such that g(a) = 0. Elements of A that are not algebraic over K are transcendental over K. A special case of an associative algebra over ${\displaystyle K}$ is an extension field ${\displaystyle L}$ of ${\displaystyle K}$.

These notions generalize the algebraic numbers and the transcendental numbers (where the field extension is C/Q, with C being the field of complex numbers and Q being the field of rational numbers).