The only non-trivial Homomorphic images of a field $F$ is $F$-------Is the statement true?
How we can prove or disprove it. I know that a field does not contain any non trivial proper ideal. and Unity will be mapped to unity itself. But with these two statements I can not progress.
Can anyone please help me?
Hint: Given a field $F$ and a homomorphism $F\to R$, the homomorphism is either injective (in which case the image is isomorphic to $F$), or it isn't. Show that if it isn't injective, then it's trivial.