Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.addVal_eq_zero_of_unit
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] (u : Rˣ),
(IsDiscreteValuationRing.addVal R) ↑u = 0- Cited by
- 4 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- ENatstatement and proof · cited by 4,985
- mul_oneproof · cited by 3,885
- Unitsstatement and proof · cited by 2,804
- IsDomainstatement and proof · cited by 2,196
- Units.valstatement and proof · cited by 1,966
- pow_zeroproof · cited by 1,094
- Irreducibleproof · cited by 496
- CharP.cast_eq_zeroproof · cited by 357
- IsDiscreteValuationRingstatement and proof · cited by 117
- AddValuationstatement · cited by 96
Cited by4
Results whose statement or proof uses this declaration.
- Ring.ord_eq_addValproof · cited by 3
- IsDiscreteValuationRing.intValuation_maximalIdealproof · cited by 3
- IsDiscreteValuationRing.addVal_eq_zero_iffproof · cited by 0
- IsDiscreteValuationRing.addVal_eq_iff_associatedproof · cited by 0