Theorems · Theorem · commutative algebra

Module.Flat.exists_factorization_of_finitePresentation

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Module.Flat R M]
  {P : Type u_3} [inst_4 : AddCommGroup P] [inst_5 : Module R P] [Module.FinitePresentation R P] (h₁ : P →ₗ[R] M),
  ∃ k h₂ h₃, h₁ = h₃ ∘ₗ h₂

Every homomorphism from a finitely presented module to a flat module factors through a finite free module.

Defined in

Mathlib.RingTheory.Flat.EquationalCriterion

Cited by

2 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleModule.FlatAddCommGroupModuleModule.FinitePresentation