Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.exists_irreducible
∀ (R : Type u) [inst : CommRing R] [inst_1 : IsDomain R] [IsDiscreteValuationRing R], ∃ ϖ, Irreducible ϖ
Uniformizers exist in a DVR.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 37 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
- Irreduciblestatement · cited by 496
- IsLocalRing.maximalIdealproof · cited by 297
- IsDiscreteValuationRingstatement and proof · cited by 117
- Submodule.IsPrincipal.principalproof · cited by 10
Cited by8
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.addVal_eq_zero_of_unitproof · cited by 4
- Ring.ord_eq_addValproof · cited by 3
- IsDiscreteValuationRing.exists_primeproof · cited by 3
- IsDiscreteValuationRing.intValuation_maximalIdealproof · cited by 3
- IsDiscreteValuationRing.exists_lift_of_le_oneproof · cited by 2
- Valued.integer.totallyBounded_iff_finite_residueFieldproof · cited by 1
- IsDiscreteValuationRing.addVal_eq_iff_associatedproof · cited by 0
- IsDiscreteValuationRing.addVal_eq_zero_iffproof · cited by 0