A

field extension *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*_{1})...(x-b_{0}), for some

*a,b*_{i}
in

*M*.

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