Theorems · Theorem · commutative algebra

LinearMap.range_codRestrict

∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_5} {M₂ : Type u_6} [inst : Semiring R] [inst_1 : Semiring R₂]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {τ₂₁ : R₂ →+* R}
  [inst_6 : RingHomSurjective τ₂₁] (p : Submodule R M) (f : M₂ →ₛₗ[τ₂₁] M) (hf : ∀ (c : M₂), f c ∈ p),
  (LinearMap.codRestrict p f hf).range = Submodule.comap p.subtype f.range

Defined in

Mathlib.Algebra.Module.Submodule.Range

Cited by

11 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModuleRingHomSurjective