Theorems · Theorem · commutative algebra

LinearIndependent.of_isLocalizedModule

∀ {R : Type u_1} (Rₛ : Type u_2) [inst : CommSemiring R] (S : Submonoid R) [inst_1 : CommSemiring Rₛ]
  [inst_2 : Algebra R Rₛ] [IsLocalization S Rₛ] {M : Type u_3} {Mₛ : Type u_4} [inst_4 : AddCommMonoid M]
  [inst_5 : Module R M] [inst_6 : AddCommMonoid Mₛ] [inst_7 : Module R Mₛ] [inst_8 : Module Rₛ Mₛ]
  [IsScalarTower R Rₛ Mₛ] (f : M →ₗ[R] Mₛ) [IsLocalizedModule S f] {ι : Type u_5} {v : ι → M},
  LinearIndependent R v → LinearIndependent Rₛ (⇑f ∘ v)

Defined in

Mathlib.RingTheory.Localization.Module

Cited by

2 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraIsLocalizationAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTowerIsLocalizedModule