
theorem hom3a:
for E,F being Field,
    f being additive multiplicative Function of E,F
holds f.(1.E) = 1.F iff f is monomorphism
proof
let E,F be Field,
    f be additive multiplicative Function of E,F;
(f.(1.E) = 0.F & f = E --> 0.F) or
(f.(1.E) = 1.F & f is monomorphism) by hom3;
hence thesis;
end;
