Let f: R --> R' be a ring homomorphism and let N be an ideal of R.
Show that f(N) is an ideal of f(R) and also show that f(N) doesn't need to be an ideal of R'
Consider defined by (evaluating polynomials at ).also show that f(N) doesn't need to be an ideal of R'
Let then .
This is not an ideal of since the complex numbers are a field.