Theorems · Definition · commutative algebra
Valuation.onQuot
{R : Type u_1} →
{Γ₀ : Type u_2} →
[inst : CommRing R] →
[inst_1 : LinearOrderedCommMonoidWithZero Γ₀] →
(v : Valuation R Γ₀) → {J : Ideal R} → J ≤ v.supp → Valuation (R ⧸ J) Γ₀The extension of valuation v on R to valuation on R / J if J ⊆ supp v.
- Defined in
- Mathlib.RingTheory.Valuation.Quotient
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Valuation.suppstatement and proof · cited by 12
- Valuation.onQuotValproof · cited by 0
Cited by6
Results whose statement or proof uses this declaration.
- AddValuation.onQuotproof · cited by 3
- Valuation.supp_quotstatement and proof · cited by 2
- Valuation.onQuot_comap_eqstatement · cited by 1
- Valuation.supp_quot_suppstatement · cited by 1
- Valuation.comap_onQuot_eqstatement and proof · cited by 1
- AddValuation.supp_quot_suppstatement · cited by 0