instFaithfulSMul — Mathlib

English

The faithful scalar action lifts to FractionRing via the base algebra and existing injections.

Русский

Достоверное скалярное действие поднимается в FractionRing через базовую алгебру и инъекции.

LaTeX

$$IsFractionRing.instFaithfulSMul R A$$

Lean4

instance [Algebra R A] [FaithfulSMul R A] : FaithfulSMul R (FractionRing A) :=
  by
  rw [faithfulSMul_iff_algebraMap_injective, IsScalarTower.algebraMap_eq R A]
  exact (FaithfulSMul.algebraMap_injective A (FractionRing A)).comp (FaithfulSMul.algebraMap_injective R A)

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