Theorems · Theorem · commutative algebra

Algebra.SubmersivePresentation.basisKaehler_apply

∀ {R : Type u_1} {S : Type u_2} {ι : Type u_3} {σ : Type u_4} [inst : CommRing R] [inst_1 : CommRing S]
  [inst_2 : Algebra R S] [inst_3 : Finite σ] (P : Algebra.SubmersivePresentation R S ι σ) (k : ↑(Set.range P.map)ᶜ),
  P.basisKaehler k = (KaehlerDifferential.D R S) (P.val ↑k)

Defined in: Mathlib.RingTheory.Smooth.StandardSmoothCotangent
Cited by: 1 results in Mathlib
Foundations: Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing Algebra Finite

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Cites20

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
Setstatement · cited by 53,352
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Set.Elemstatement and proof · cited by 7,166
Set.rangestatement and proof · cited by 4,705
Finitestatement and proof · cited by 3,029
Compl.complstatement and proof · cited by 2,925
Module.Basisstatement · cited by 1,477
Derivationstatement · cited by 293
KaehlerDifferentialstatement · cited by 204
Algebra.Generators.valstatement and proof · cited by 115

Cited by1

Results whose statement or proof uses this declaration.

Algebra.IsStandardSmooth.iff_exists_basis_kaehlerDifferentialproof · cited by 1