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  3. exercise 2 let r s be commutative rings and let...

Question: exercise 2 let r s be commutative rings and let...

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Exercise 2. Let R, S be commutative rings, and let f : R → S be a ring-homomorphism. Let Q be a prime ideal of S, and set P = f-1(Q).

(1) Show that there exists an injective homomorphism R/P → S/Q.

(2) Show that P is a prime ideal of R.

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