Theorems · Definition · commutative algebra

Valuation.map

{R : Type u_3} →
  {Γ₀ : Type u_4} →
    {Γ'₀ : Type u_5} →
      [inst : Ring R] →
        [inst_1 : LinearOrderedCommMonoidWithZero Γ₀] →
          [inst_2 : LinearOrderedCommMonoidWithZero Γ'₀] →
            (f : Γ₀ →*₀ Γ'₀) → Monotone ⇑f → Valuation R Γ₀ → Valuation R Γ'₀

A ≤-preserving group homomorphism Γ₀ → Γ'₀ induces a map Valuation R Γ₀ → Valuation R Γ'₀.

Defined in

Mathlib.RingTheory.Valuation.Basic

Cited by

4 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

RingLinearOrderedCommMonoidWithZeroLinearOrderedCommMonoidWithZero