Theorems · Theorem · commutative algebra

Valuation.HasExtension.mk_smul_mk

∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] {ΓR : Type u_6}
  {ΓA : Type u_7} [inst_3 : LinearOrderedCommGroupWithZero ΓR] [inst_4 : LinearOrderedCommGroupWithZero ΓA]
  {vR : Valuation R ΓR} {vA : Valuation A ΓA} [inst_5 : vR.HasExtension vA] (r : R) (hr : r ∈ vR.integer) (a : A)
  (ha : a ∈ vA.integer), ⟨r, hr⟩ • ⟨a, ha⟩ = ⟨r • a, ⋯⟩

Defined in

Mathlib.RingTheory.Valuation.Extension

Cited by

0 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingRingAlgebraLinearOrderedCommGroupWithZeroLinearOrderedCommGroupWithZeroValuation.HasExtension