Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.exists_prime
∀ (R : Type u) [inst : CommRing R] [inst_1 : IsDomain R] [IsDiscreteValuationRing R], ∃ ϖ, Prime ϖ
Uniformizers exist in a DVR.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Primestatement · cited by 277
- IsDiscreteValuationRingstatement and proof · cited by 117
- irreducible_iff_primeproof · cited by 15
- IsDiscreteValuationRing.exists_irreducibleproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.addVal_eq_top_iffproof · cited by 4
- IsDiscreteValuationRing.addVal_defproof · cited by 3
- IsDiscreteValuationRing.addVal_le_iff_dvdproof · cited by 1