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  • https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Rings_with_Inquiry_(Janssen_and_Lindsey)/03%3A_Factorization/3.02%3A_Factorization_in_Euclidean_Domains
    In this section, our explorations of the structural arithmetic properties that guarantee unique factorization culminate in Theorem 3.2.7 . Specifically, we'll see that all Euclidean domains possess t...In this section, our explorations of the structural arithmetic properties that guarantee unique factorization culminate in Theorem 3.2.7 . Specifically, we'll see that all Euclidean domains possess the unique factorization property. To prove this theorem, we will rely in part on an interesting property of chains of ideals in Euclidean domains.

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