# Algebraic element

In mathematics, if *L* is a field extension of *K*, then an element *a* of *L* is called an **algebraic element** over *K*, or just **algebraic over** *K*, if there exists some non-zero polynomial *g*(*x*) with coefficients in *K* such that *g*(*a*) = 0. Elements of *L* which are not algebraic over *K* are called **transcendental** over *K*.

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