Theorems · Theorem · commutative algebra

Module.finitePresentation_of_free_of_surjective

∀ {R : Type u_1} {M : Type u_2} {N : Type u_3} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : AddCommGroup N] [inst_4 : Module R N] [Module.Free R M] [Module.Finite R M] (l : M →ₗ[R] N),
  Function.Surjective ⇑l → l.ker.FG → Module.FinitePresentation R N

Defined in

Mathlib.Algebra.Module.FinitePresentation

Cited by

3 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddCommGroupModuleModule.FreeModule.Finite