Theorems · Theorem · commutative algebra
Valuation.Uniformizer.is_generator
∀ {Γ : Type u_1} [inst : LinearOrderedCommGroupWithZero Γ] {K : Type u_2} [inst_1 : Field K] {v : Valuation K Γ}
[hv : v.IsRankOneDiscrete] (π : v.Uniformizer), IsLocalRing.maximalIdeal ↥v.valuationSubring = Ideal.span {π.val}- Cited by
- 4 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Top.topproof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Idealstatement · cited by 4,748
- Monoidproof · cited by 3,887
- one_mulproof · cited by 2,841
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitproof · cited by 1,602
- pow_zeroproof · cited by 1,094
- Ideal.spanstatement and proof · cited by 948
- Valuationstatement and proof · cited by 823
Cited by4
Results whose statement or proof uses this declaration.
- Valuation.ideal_isPrincipalproof · cited by 1
- Valuation.IsUniformizer.is_generatorproof · cited by 0
- Valuation.pow_Uniformizer_is_pow_generatorproof · cited by 0
- Valuation.isUniformizer_of_maximalIdeal_eq_spanproof · cited by 0