Theorems · Theorem · commutative algebra

Module.exists_basis_of_span_of_flat

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsLocalRing R]
  [Module.FinitePresentation R M] [Module.Flat R M] {ι : Type u} (v : ι → M),
  Submodule.span R (Set.range v) = ⊤ → ∃ κ a b, ∀ (i : κ), b i = v (a i)

Defined in

Mathlib.RingTheory.LocalRing.Module

Cited by

1 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleIsLocalRingModule.FinitePresentationModule.Flat