Theorems · Theorem · commutative algebra

Algebra.IsStandardSmooth.out

∀ {R : Type u} {S : Type v} {inst : CommRing R} {inst_1 : CommRing S} {inst_2 : Algebra R S}
  [self : Algebra.IsStandardSmooth R S],
  ∃ ι σ, ∃ (x : Finite σ), Finite ι ∧ Nonempty (Algebra.SubmersivePresentation R S ι σ)

Defined in: Mathlib.RingTheory.Smooth.StandardSmooth
Cited by: 1 results in Mathlib
Foundations: Depth 7 from the axioms · uses no axioms
Assumes: Algebra.IsStandardSmooth

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

CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Finitestatement · cited by 3,029
Algebra.SubmersivePresentationstatement · cited by 52
Algebra.IsStandardSmoothstatement and proof · cited by 17

Cited by1

Results whose statement or proof uses this declaration.

Algebra.IsStandardSmooth.iff_exists_basis_kaehlerDifferentialproof · cited by 1