Theorems · Theorem · commutative algebra
Valuation.IsRankOneDiscrete.generator_eq_exp_neg_one_of_mem_range
∀ {A : Type u_2} [inst : Ring A] {v : Valuation A (WithZero (Multiplicative ℤ))} [hv : v.IsRankOneDiscrete],
WithZero.exp (-1) ∈ Set.range ⇑v →
Valuation.IsRankOneDiscrete.generator v =
Units.mk0 (WithZero.exp (-1)) Valuation.IsRankOneDiscrete.generator_eq_exp_neg_one_of_mem_range._proof_1The generator of a discrete valuation in ℤᵐ⁰ that contains exp (-1) in its range
is equal to exp (-1).
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Ringstatement and proof · cited by 7,463
- Set.rangestatement and proof · cited by 4,705
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Unitsstatement and proof · cited by 2,804
- Nat.cast_oneproof · cited by 2,501
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
- neg_negproof · cited by 960
- Multiplicativestatement and proof · cited by 875
Cited by2
Results whose statement or proof uses this declaration.
- Valuation.IsRankOneDiscrete.generator_eq_exp_neg_one_of_surjectiveproof · cited by 2
- IsDedekindDomain.HeightOneSpectrum.intValuation_uniformizerproof · cited by 0