Theorems · Theorem · commutative algebra

IsLocalizedModule.restrictScalars_iff

∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_2} [inst_1 : AddCommMonoid M] {A : Type u_5}
  [inst_2 : CommSemiring A] [inst_3 : Algebra R A] [inst_4 : Module R M] (S : Submonoid R) {N : Type u_6}
  [inst_5 : AddCommMonoid N] [inst_6 : Module R N] [inst_7 : Module A M] [inst_8 : Module A N]
  [inst_9 : IsScalarTower R A M] [inst_10 : IsScalarTower R A N] (f : M →ₗ[A] N),
  IsLocalizedModule (Algebra.algebraMapSubmonoid A S) f ↔ IsLocalizedModule S (↑R f)

Defined in

Mathlib.Algebra.Module.LocalizedModule.Basic

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidCommSemiringAlgebraModuleAddCommMonoidModuleModuleModuleIsScalarTowerIsScalarTower