Let F be a field and R be a ring. Prove that any homomorphism of rings f : F → R
is injective
I have no idea where to start!!! please please help me!
For all nonzero x in F,
1 = f(1) = f(x x^(-1)) = f(x) f(x^(-1)),
so f(x) cannot be zero. Therefore, f is injective.
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Verified answer
For all nonzero x in F,
1 = f(1) = f(x x^(-1)) = f(x) f(x^(-1)),
so f(x) cannot be zero. Therefore, f is injective.