1. Math
2. Algebra
3. exercise 2 let r s be commutative rings and let...

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

###### Question details

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.