Theorems · Inductive type · commutative algebra

Valuation.HasExtension

{R : Type u_1} →
  {A : Type u_2} →
    {ΓR : Type u_3} →
      {ΓA : Type u_4} →
        [inst : CommRing R] →
          [inst_1 : Ring A] →
            [inst_2 : LinearOrderedCommMonoidWithZero ΓR] →
              [inst_3 : LinearOrderedCommMonoidWithZero ΓA] → [Algebra R A] → Valuation R ΓR → Valuation A ΓA → Prop

The class Valuation.HasExtension vR vA states that the valuation vA on A is an extension of the valuation vR on R. More precisely, vR is equivalent to the comap of the valuation vA.

Defined in

Mathlib.RingTheory.Valuation.Extension

Cited by

17 results in Mathlib

Foundations

Depth 6 from the axioms · uses no axioms

Assumes

CommRingRingLinearOrderedCommMonoidWithZeroLinearOrderedCommMonoidWithZeroAlgebra