Theorems · Definition · commutative algebra
Valuation.ltAddSubgroup
{R : Type u_3} →
{Γ₀ : Type u_4} →
[inst : Ring R] → [inst_1 : LinearOrderedCommGroupWithZero Γ₀] → Valuation R Γ₀ → Γ₀ˣ → AddSubgroup RThe subgroup of elements whose valuation is less than a certain unit.
- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Set.ofPredproof · cited by 6,101
- AddSubgroupstatement · cited by 3,232
- 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
Cited by14
Results whose statement or proof uses this declaration.
- Valuation.subgroups_basisstatement and proof · cited by 5
- Valuation.ltIdealproof · cited by 4
- Valuation.ltSubmoduleproof · cited by 4
- Valuation.coe_ltAddSubgroupstatement and proof · cited by 3
- Valuation.isClosed_ballproof · cited by 2
- Valuation.toUniformSpace_eqstatement and proof · cited by 2
- Valuation.ltAddSubgroup_le_leAddSubgroupstatement and proof · cited by 1
- Valuation.ltAddSubgroup_monotonestatement · cited by 1
- Valued.toUniformSpace_eqstatement and proof · cited by 1
- Valued.isClosed_ballproof · cited by 1
- Valued.cauchy_iffproof · cited by 0
- Valuation.cauchy_iffproof · cited by 0