Theorems · Theorem · ring theory

LinearMap.injective_of_comp_eq_id

∀ {R : Type u_1} {S : Type u_5} {M : Type u_8} {M₂ : Type u_10} [inst : Semiring R] [inst_1 : Semiring S]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module S M₂] {σ : R →+* S}
  {σ' : S →+* R} [inst_6 : RingHomInvPair σ σ'] (f : M →ₛₗ[σ] M₂) (g : M₂ →ₛₗ[σ'] M),
  g ∘ₛₗ f = LinearMap.id → Function.Injective ⇑f

Defined in

Mathlib.Algebra.Module.LinearMap.Defs

Cited by

9 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModuleRingHomInvPair