Principal Ideal Domain is Unique Factorization Domain
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This theorem requires a proof.
Need to prove that the factorization is unique
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Theorem
Every principal ideal domain is a unique factorization domain.
Proof
From Element of Principal Ideal Domain is Finite Product of Irreducible Elements, each element which is neither $0$ nor a unit of a principal ideal domain has a factorization of irreducible elements.
Need to prove that the factorization is unique
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
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Sources
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 62$. Factorization in an integral domain