Theorems · Theorem · commutative algebra

LinearMap.surjective_of_surjective_comp_mkQ

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Type u_3}
  [inst_3 : AddCommGroup N] [inst_4 : Module R N] [Module.Finite R N] (f : M →ₗ[R] N),
  ∀ I ≤ ⊥.jacobson, Function.Surjective ⇑((I • ⊤).mkQ ∘ₗ f) → Function.Surjective ⇑f

Defined in

Mathlib.RingTheory.Nakayama

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommRingAddCommGroupModuleAddCommGroupModuleModule.Finite