Suppose that R and S are commutative rings with unities.
Chapter 15, Problem 47E(choose chapter or problem)
Problem 47E
Suppose that R and S are commutative rings with unities. Let f be a ring homomorphism from R onto S and let A be an ideal of S.
a. If A is prime in S, show that Φ–1(A) = {x∈R | f(x) ∈ A} is prime in R.
b. If A is maximal in S, show that Φ–1(A) is maximal in R.
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