Theorems · Theorem · commutative algebra

IsLocalization.map_smul

∀ {R : Type u_1} [inst : CommSemiring R] {M : Submonoid R} {S : Type u_2} [inst_1 : CommSemiring S]
  [inst_2 : Algebra R S] {P : Type u_3} [inst_3 : CommSemiring P] [inst_4 : IsLocalization M S] {g : R →+* P}
  {T : Submonoid P} {Q : Type u_4} [inst_5 : CommSemiring Q] [inst_6 : Algebra P Q] [inst_7 : IsLocalization T Q]
  (hy : M ≤ Submonoid.comap g T) (x : S) (z : R),
  (IsLocalization.map Q g hy) (z • x) = g z • (IsLocalization.map Q g hy) x

Defined in

Mathlib.RingTheory.Localization.Defs

Cited by

2 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringAlgebraCommSemiringIsLocalizationCommSemiringAlgebraIsLocalization