Theorems · Theorem · commutative algebra

Module.Finite.exists_free_surjective

∀ (R : Type u) (S : Type u_1) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [Module.Finite R S],
  ∃ S' x x_1,
    ∃ (_ : Module.Finite R S') (_ : Module.Free R S') (_ : Algebra.FinitePresentation R S'), ∃ f, Function.Surjective ⇑f

EGA IV₁, 1.4.7.1

Defined in: Mathlib.RingTheory.Finiteness.ModuleFinitePresentation
Cited by: 1 results in Mathlib
Foundations: Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing Algebra Module.Finite

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Cites49

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
CommRingstatement and proof · cited by 17,173
Finsetproof · cited by 13,712
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Top.topproof · cited by 9,680
SetLike.coeproof · cited by 8,199
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Algebra.algebraMapproof · cited by 4,706
Set.rangeproof · cited by 4,705
AlgHomstatement and proof · cited by 3,236
LE.le.transproof · cited by 3,151
Submodule.spanproof · cited by 1,504

Cited by1

Results whose statement or proof uses this declaration.

Module.FinitePresentation.of_finite_of_finitePresentationproof · cited by 2