normal closure

Let K be an extension fieldMathworldPlanetmath of F. A normal closurePlanetmathPlanetmathPlanetmath of K/F is a field LK that is a normal extensionMathworldPlanetmath of F and is minimalPlanetmathPlanetmath in that respect, i.e. no proper subfield of L containing K is normal over F. If K is an algebraic extensionMathworldPlanetmath of F, then a normal closure for K/F exists and is unique up to isomorphismPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath.

Title normal closure
Canonical name NormalClosure
Date of creation 2013-03-22 13:09:36
Last modified on 2013-03-22 13:09:36
Owner scanez (1021)
Last modified by scanez (1021)
Numerical id 5
Author scanez (1021)
Entry type Definition
Classification msc 12F10