3. Consider the function f: ZQ defined by f(n) = n. a) Prove f is a ring homomorphism. b) Find the image of f. Recall, im f = {q EQ | 3n e Z such that f(n) = q}. c) Is im f an ideal in Q? If yes, prove it. If no, provide a counterexample. d) Show that im f is closed under addition and multiplication. e) Look at what you have done in (c) and (d). Fill in the blanks based on your answers. Conjecture: im f is NOT an in Q but im f is a of Q.

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