Theorems · Definition · commutative algebra
Valuation.leAddSubgroup
{R : Type u_3} →
{Γ₀ : Type u_4} → [inst : Ring R] → [inst_1 : LinearOrderedCommGroupWithZero Γ₀] → Valuation R Γ₀ → Γ₀ → AddSubgroup RThe subgroup of elements whose valuation is less than or equal to a certain value.
- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 4 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.
Cites6
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
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
Cited by6
Results whose statement or proof uses this declaration.
- Valuation.leIdealproof · cited by 7
- Valuation.leSubmoduleproof · cited by 7
- Valuation.ltAddSubgroup_le_leAddSubgroupstatement · cited by 1
- Valuation.leAddSubgroup_monotonestatement · cited by 1
- Valuation.mem_leAddSubgroup_iffstatement · cited by 0
- Valuation.leAddSubgroup_zerostatement · cited by 0