Theorems · Theorem · ring theory

LinearMap.isScalarTower_of_injective

∀ {M : Type u_8} {M₂ : Type u_10} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid M₂] (R : Type u_14) {S : Type u_15}
  [inst_2 : Semiring S] [inst_3 : SMul R M] [inst_4 : Module S M] [inst_5 : SMul R M₂] [inst_6 : Module S M₂]
  [inst_7 : SMul R S] [LinearMap.CompatibleSMul M M₂ R S] [IsScalarTower R S M₂] (f : M →ₗ[S] M₂),
  Function.Injective ⇑f → IsScalarTower R S M

Defined in

Mathlib.Algebra.Module.LinearMap.Defs

Cited by

2 results in Mathlib

Foundations

Depth 23 from the axioms · uses no axioms

Assumes

AddCommMonoidAddCommMonoidSemiringSMulModuleSMulModuleSMulLinearMap.CompatibleSMulIsScalarTower