An algebraic field extension is said to be normal if is the splitting field of a family of polynomials in .

**Equivalent Properties**

The normality of is equivalent to either of the following properties. Let be an algebraic closure of containing .

1) Every embedding of in that restricts to the identity on , satisfies . In other words, , is an automorphism of over .

2) Every irreducible polynomial in that has one root in , has all of its roots in , that is, it decomposes into linear factors in . (One says that the polynomial splits in .)