Mathematics · Ring Theory

Let R and S be commutative rings with unity, f : R → S be a surjective ring homomorphism, and Q &sube; S be a non-zero prime ideal. Which of the following statements is true?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Correct answer

f −1 (Q) is a non-zero prime ideal in R

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Let R and S be commutative rings with unity, f : R &rarr; S be a surjective ring homomorphism, and Q &sube; S be a non-zero prime ideal. Which of the following statements is true?