Mathematics · Abstract Algebra
Let R be a principal ideal domain (PID) with a unique maximal ideal. Which of the following statements is necessarily true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Every non-zero quotient ring S of R has a unique maximal ideal which is principal✓
- 2R has uncountably many ideals
- 3There exists a quotient ring S of R and an ideal I ⊆ S which is not principal
- 4Every quotient ring of R is a principal ideal domain
Correct answer
Every non-zero quotient ring S of R has a unique maximal ideal which is principal
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