Normal extension

In algebra, a normal extension of fields is a field extension E/F which contains all the roots of an irreducible polynomial if it contains one such root.

A normal closure is a normal extension N/F with the property that no subfield of N is a normal extension of F. Given any finite degree extension E/F there is a minimal finite degree normal extension N containing E: this will be "the" normal closure of E over F; any two normal closures are L-isomorphic.