Theorems · Theorem · commutative algebra
Valuation.IsRankOneDiscrete.exists_generator_lt_one
∀ {Γ : Type u_1} [inst : LinearOrderedCommGroupWithZero Γ] {A : Type u_2} [inst_1 : Ring A] (v : Valuation A Γ)
[v.IsRankOneDiscrete], ∃ γ, Subgroup.zpowers γ = (MonoidWithZeroHom.ofClass v).valueGroup ∧ γ < 1- Cited by
- 3 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Subgroupstatement · cited by 3,593
- Unitsstatement · cited by 2,804
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MonoidWithZeroHom.ofClassstatement · cited by 204
- Subgroup.zpowersstatement · cited by 204
- MonoidWithZeroHom.valueGroupstatement · cited by 170
- Valuation.IsRankOneDiscretestatement and proof · cited by 53
- Valuation.IsRankOneDiscrete.exists_generator_lt_one'proof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Valuation.IsRankOneDiscrete.generatorproof · cited by 24
- Valuation.IsRankOneDiscrete.generator_zpowers_eq_valueGroupproof · cited by 4
- Valuation.IsRankOneDiscrete.generator_lt_oneproof · cited by 4
- Valuation.IsRankOneDiscrete.generator'_lt_oneproof · cited by 1