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(a) Let f : R > R' be a ring homomorphism. i. If I is a principal ideal of R, show that f (I )

(a) Let f : R > R' be a ring homomorphism. i. If I is a principal ideal of R, show that f (I ) is a principal ideal of f (R). ii. Must f _1(J ) a principal if J is a principal ideal of R\"? Justify your

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