Mathlib Map

Theorems · Inductive type · commutative algebra

Valuation

(R : Type u_3) → (Γ₀ : Type u_4) → [LinearOrderedCommMonoidWithZero Γ₀] → [Ring R] → Type (max u_3 u_4)

The type of Γ₀-valued valuations on R. When you extend this structure, make sure to extend ValuationClass.

Defined in
Mathlib.RingTheory.Valuation.Basic
Cited by
823 results in Mathlib
Foundations
Depth 1 from the axioms, rests on 3 definitions · uses no axioms
Assumes
LinearOrderedCommMonoidWithZeroRing

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by975

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 975.