Theorems · Definition · commutative algebra

AddValuation.map

{R : Type u_3} →
  {Γ₀ : Type u_4} →
    {Γ'₀ : Type u_5} →
      [inst : Ring R] →
        [inst_1 : LinearOrderedAddCommMonoidWithTop Γ₀] →
          [inst_2 : LinearOrderedAddCommMonoidWithTop Γ'₀] →
            (f : Γ₀ →+ Γ'₀) → f ⊤ = ⊤ → Monotone ⇑f → AddValuation R Γ₀ → AddValuation R Γ'₀

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

Defined in

Mathlib.RingTheory.Valuation.Basic

Cited by

2 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Quot.sound

Assumes

RingLinearOrderedAddCommMonoidWithTopLinearOrderedAddCommMonoidWithTop