
theorem uu4:
for F being Field,
    E being FieldExtension of F
for a being F-algebraic Element of E
for p being irreducible Element of the carrier of Polynom-Ring F
st Ext_eval(p,a) = 0.E holds MinPoly(a,F) = NormPolynomial p
proof
let F be Field, E be FieldExtension of F;
let a be F-algebraic Element of E;
let p be irreducible Element of the carrier of Polynom-Ring F;
set q = NormPolynomial p;
assume Ext_eval(p,a) = 0.E;
then Ext_eval(q,a) = 0.E by FIELD_6:25;
hence thesis by RING_4:28,FIELD_6:52;
end;
