Principal Ideal Domain is Unique Factorization Domain
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Theorem
Every principal ideal domain is a unique factorization domain.
Proof
From Elements of Principal Ideal Domain are Finite Product of Irreducible, 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
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Sources
- Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 62$ (mentioned)
