Mathematics · Abstract Algebra
Let R be an integral domain in which every non-zero non-unit element can be written as a product of irreducible elements. Assume further that every irreducible element in R is prime. Which of the following statements must be true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1R is necessarily a Euclidean Domain
- 2R is a Unique Factorization Domain✓
- 3R must contain zero divisors
- 4R is necessarily a Principal Ideal Domain
Correct answer
R is a Unique Factorization Domain
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