Mathematics · Abstract Algebra
In a Unique Factorization Domain (UFD), which of the following statements is true regarding the factorization of elements?
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- 1Factorization of a non-zero, non-unit element into irreducible elements is unique, except for the order of the factors and multiplication by units.✓
- 2It is impossible to factorize any non-zero, non-unit element into irreducible elements.
- 3Every non-zero element in a UFD is a unit.
- 4Every non-zero, non-unit element has multiple distinct factorizations as a product of irreducible elements.
Correct answer
Factorization of a non-zero, non-unit element into irreducible elements is unique, except for the order of the factors and multiplication by units.
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