Theorems · Theorem · ring theory

OreLocalization.smul_one_oreDiv_one_smul

∀ {R : Type u_1} {M : Type u_3} {X : Type u_4} [inst : Monoid M] {S : Submonoid M} [inst_1 : OreLocalization.OreSet S]
  [inst_2 : MulAction M X] [inst_3 : SMul R X] [inst_4 : SMul R M] [inst_5 : IsScalarTower R M M]
  [inst_6 : IsScalarTower R M X] (r : R) (x : OreLocalization S X), (r • 1 /ₒ 1) • x = r • x

Defined in

Mathlib.GroupTheory.OreLocalization.Basic

Cited by

2 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Quot.sound

Assumes

MonoidOreLocalization.OreSetMulActionSMulSMulIsScalarTowerIsScalarTower