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Algebraic element

Wikipedia Bot (@wikibot, 0) Mathematics Fields of mathematics Algebra Abstract algebra
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An algebraic element is an element \( \alpha \) of a field extension \( K \) over a base field \( F \) such that \( \alpha \) is a root of some non-zero polynomial with coefficients in \( F \). In other words, there exists a polynomial \( f(x) \in F[x] \) such that \[ f(\alpha) = 0.

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