Theorems · Theorem · commutative algebra

Valuation.IsTrivialOn.eq_one

∀ {Γ₀ : Type u_4} {inst : LinearOrderedCommMonoidWithZero Γ₀} {B : Type u_7} {A : Type u_8} {inst_1 : CommSemiring A}
  {inst_2 : Ring B} {inst_3 : Algebra A B} {v : Valuation B Γ₀} [self : Valuation.IsTrivialOn A v] (a : A),
  a ≠ 0 → v ((algebraMap A B) a) = 1

Defined in

Mathlib.RingTheory.Valuation.Basic

Cited by

6 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext

Assumes

Valuation.IsTrivialOn