Theorems · Theorem · commutative algebra
Valuation.IsRankOneDiscrete.valueGroup_genLTOne_eq_generator
∀ {Γ : Type u_1} [inst : LinearOrderedCommGroupWithZero Γ] {A : Type u_2} [inst_1 : Ring A] (v : Valuation A Γ)
[inst_2 : v.IsRankOneDiscrete],
LinearOrderedCommGroup.Subgroup.genLTOne (MonoidWithZeroHom.ofClass v).valueGroup =
Valuation.IsRankOneDiscrete.generator v- Cited by
- 4 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Unitsstatement · cited by 2,804
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MonoidWithZeroHom.ofClassstatement and proof · cited by 204
- MonoidWithZeroHom.valueGroupstatement and proof · cited by 170
- Valuation.IsRankOneDiscretestatement and proof · cited by 53
- Valuation.IsRankOneDiscrete.generatorstatement · cited by 24
- LinearOrderedCommGroup.Subgroup.genLTOnestatement · cited by 12
- LinearOrderedCommGroup.Subgroup.genLTOne_uniqueproof · cited by 5
- Valuation.IsRankOneDiscrete.generator_lt_oneproof · cited by 4
- Valuation.IsRankOneDiscrete.generator_zpowers_eq_valueGroupproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Valuation.IsRankOneDiscrete.generator_eq_exp_neg_one_of_mem_rangeproof · cited by 2
- Valuation.exists_isUniformizer_of_isCyclic_of_nontrivialproof · cited by 2
- RatFunc.uniformizingPolynomial_isUniformizerproof · cited by 1
- Valuation.IsUniformizer.zpowers_eq_valueGroupproof · cited by 1