Let K be an extension fieldMathworldPlanetmath of F and let aK.

If there is a nonzero polynomialPlanetmathPlanetmath fF[x] such that f(a)=0 (in K) we say that a is algebraic over F.

For example, 2 is algebraic over since there is a nonzero polynomial with rational coefficients, namely f(x)=x2-2, such that f(2)=0.

If all elements of K are algebraic over F, one says that the field extension K/F is algebraicMathworldPlanetmath.

Title algebraic
Canonical name Algebraic
Date of creation 2013-11-05 18:32:06
Last modified on 2013-11-05 18:32:06
Owner drini (3)
Last modified by pahio (2872)
Numerical id 8
Author drini (2872)
Entry type Definition
Classification msc 13B05
Classification msc 11R04
Classification msc 11R32
Related topic AlgebraicNumber
Related topic FiniteExtension
Related topic ProofOfTranscendentalRootTheorem