Theorems · Theorem · linear algebra

Submodule.range_mapQ

∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (p : Submodule R M)
  {R₂ : Type u_3} {M₂ : Type u_4} [inst_3 : Ring R₂] [inst_4 : AddCommGroup M₂] [inst_5 : Module R₂ M₂] {τ₁₂ : R →+* R₂}
  (q : Submodule R₂ M₂) [inst_6 : RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂) (h : p ≤ Submodule.comap f q),
  (p.mapQ q f h).range = Submodule.map q.mkQ f.range

Defined in

Mathlib.LinearAlgebra.Quotient.Basic

Cited by

3 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleRingAddCommGroupModuleRingHomSurjective