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-b1)...(x-b0), for some
a,bi
in
M.
For example, the fundamental theorem of algebra tells us that
C is a normal extension of Q.