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Noncommutative unique factorization domain (view)
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alternate case: unique factorization domain
Symbolic method (combinatorics)
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the symmetric group S n {\displaystyle S_{n}} , which form a unique factorization domain. (The orbits with respect to two groups from the same conjugacy
Dimension theory (algebra)
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which is absurd. Q.E.D. Corollary—A regular local ring is a unique factorization domain. Proof: Let R be a regular local ring. Then gr R ≃ k [ x 1