normal extension

A field extension K/F is normal if every irreducible polynomialMathworldPlanetmath fF[x] which has at least one root in K splits (factors into a productMathworldPlanetmathPlanetmath of linear factors) in K[x].

An extensionPlanetmathPlanetmath K/F of finite degree is normal if and only if there exists a polynomialMathworldPlanetmathPlanetmathPlanetmath pF[x] such that K is the splitting fieldMathworldPlanetmath for p over F.

Title normal extensionMathworldPlanetmath
Canonical name NormalExtension
Date of creation 2013-03-22 12:08:15
Last modified on 2013-03-22 12:08:15
Owner djao (24)
Last modified by djao (24)
Numerical id 10
Author djao (24)
Entry type Definition
Classification msc 12F10
Synonym normal
Related topic SplittingField