A normal extension is the splitting field for a collection of polynomials. In the case of a finite algebraic extension, only one polynomial is necessary.
Normal Extension
See also
Extension Field, Galois Extension Field, Splitting FieldThis entry contributed by Todd Rowland
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Rowland, Todd. "Normal Extension." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/NormalExtension.html