Characterisation of UFDs
From ProofWiki
Theorem
Let $A$ be an integral domain.
Then the following are equivalent:
- 1. $A$ is a unique factorisation domain
- 2. $A$ is a GCD domain satisfying the ascending chain condition on principal ideals.
- 3. $A$ satisfies the ascending chain condition on principal ideals and every irreducible element of $A$ is prime.
Proof
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