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 g ( x ) ∈ K [ x ] {\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 K {\displaystyle K} is an extension field L {\displaystyle L} of K {\displaystyle K} .
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 g ( x ) ∈ K [ x ] {\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 K {\displaystyle K} is an extension field L {\displaystyle L} of K {\displaystyle K} .
Source: Wikipedia "Algebraic element" · CC BY-SA 4.0
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