In abstract algebra, an algebraic field extension L/K is said to be normal if L is the splitting field of a family of polynomials in K[X].
The following conditions are equivalent to L/K being a normal extension:
- Let Ka an algebraic closure of K containing L. Every embedding σ of L in Ka such that σ restricts to the identity on K, verifies σ(L)=L. In other words, σ is an automophism of L over K.
For example, Q(√2)/Q is a normal extension, but Q(4√2)/Q is not a normal extension since it is missing some roots of X4-2.