*M*of

*K*is called normal iff whenever an irreducible polynomial

*f(x)*in

*K[x]*has a zero in

*M*then it can be factorised into linear factors in

*M[x]*, that is we can write

*f(x)=a(x-b*, for some

_{1})...(x-b_{0})*a,b*in

_{i}*M*.

For example, the fundamental theorem of algebra tells us that
**C** is a normal extension of **Q**.