An algebraic extension 
of a field 
has every element of 
algebraic over 
(i.e., each element is the root of a nonzero polynomial with
coefficients in 
).
Algebraic Extension
See also
Galois Extension FieldThis entry contributed by Nicolas Bray
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Cite this as:
Weisstein, Eric W., with contributions by Nicolas Bray. "Algebraic Extension." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AlgebraicExtension.html