Theorems · Definition · commutative algebra
Valuation.supp
{R : Type u_3} →
{Γ₀ : Type u_4} → [inst : CommRing R] → [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] → Valuation R Γ₀ → Ideal RThe support of a valuation v : R → Γ₀ is the ideal of R where v vanishes.
- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext
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
- CommRingstatement and proof · cited by 17,173
- Set.ofPredproof · cited by 6,101
- Idealstatement · cited by 4,748
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
Cited by16
Results whose statement or proof uses this declaration.
- AddValuation.suppproof · cited by 7
- Valuation.onQuotstatement and proof · cited by 5
- Valuation.extendToLocalizationstatement and proof · cited by 4
- IsDedekindDomain.HeightOneSpectrum.valuation_defstatement · cited by 3
- Valuation.comap_suppstatement and proof · cited by 2
- Valuation.self_le_supp_comapstatement and proof · cited by 2
- Valuation.supp_quotstatement and proof · cited by 2
- Valuation.mem_supp_iffstatement · cited by 2
- Valuation.onQuot_comap_eqstatement and proof · cited by 1
- Valuation.map_add_suppstatement and proof · cited by 1
- Valuation.supp_quot_suppstatement and proof · cited by 1
- Valuation.extendToLocalization_apply_map_applystatement and proof · cited by 1