Back Element algebraic Catalan Algebraický prvek Czech Algebraisches Element German Αλγεβρικό στοιχείο Greek Algebra elemento Esperanto Elemento algebraico Spanish عضو جبری Persian Élément algébrique French איבר אלגברי HE Algebral elemento IO
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In mathematics, if L is an extension field 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 that are not algebraic over K are called transcendental over 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).