Show that each homomorphism of a field is either one to one or maps everything to 0..
the one to one part is easy, i need the second one..
also, how will i define ? is it like this?
let F , F' be fields and define ... i am not sure..
Thus, if is a homomrophism from the field then is an ideal. But a field can only has or itself as an ideal. Thus, in the first case the map is one-to-one because the kernel is trivial. And in the other case the map collapses everything into 0 because it is the full field.