How do I Show that either f(1)=0 or f(1)=1 ii) Show that either f maps each element of F to 0 or f is injective.
Let f be a homomorphism from a field F onto an integral domain D…see extended details? i) Show that either f(1)=0 or f(1)=1 ii) Show that either f maps each element of F to 0 or f is injective.
This is for modern algebra. Do not understand it. Someone told me to use kernel, but we have not studied that yet so if someone could explain this without kernel, that would be great.
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