Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.ofHasUnitMulPowIrreducibleFactorization
∀ {R : Type u} [inst : CommRing R] [inst_1 : IsDomain R],
IsDiscreteValuationRing.HasUnitMulPowIrreducibleFactorization R → IsDiscreteValuationRing RAn integral domain in which there is an irreducible element p
such that every nonzero element is associated to a power of p
is a discrete valuation ring.
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- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- IsDomainstatement and proof · cited by 2,196
- Irreducibleproof · cited by 496
- Associatedproof · cited by 296
- UniqueFactorizationMonoidproof · cited by 279
- IsDiscreteValuationRingstatement · cited by 117
- IsDiscreteValuationRing.HasUnitMulPowIrreducibleFactorizationstatement and proof · cited by 5
- IsDiscreteValuationRing.of_ufd_of_unique_irreducibleproof · cited by 1
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