Principal Ideal Domain is Unique Factorization Domain
Jump to navigation
Jump to search
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.
 | This theorem requires a proof. In particular: Need to prove that the factorization is unique You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Sources
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 62$. Factorization in an integral domain