Theorems · Theorem · commutative algebra
Valuation.IsUniformizer.zpowers_eq_valueGroup
∀ {Γ : Type u_1} [inst : LinearOrderedCommGroupWithZero Γ] {A : Type u_2} [inst_1 : Ring A] {v : Valuation A Γ}
[hv : v.IsRankOneDiscrete] {π : A} (hπ : v.IsUniformizer π),
(MonoidWithZeroHom.ofClass v).valueGroup = Subgroup.zpowers (Units.mk0 (v π) ⋯)- Cited by
- 1 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.
Cites22
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
- Ringstatement and proof · cited by 7,463
- Groupproof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- Units.valproof · cited by 1,966
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MonoidWithZeroHom.ofClassstatement and proof · cited by 204
- Subgroup.zpowersstatement and proof · cited by 204
- Units.mk0statement and proof · cited by 181
- MonoidWithZeroHom.valueGroupstatement and proof · cited by 170
Cited by1
Results whose statement or proof uses this declaration.
- Valuation.exists_pow_Uniformizerproof · cited by 3