Theorems · Theorem · field theory
Algebra.FormallySmooth.of_algebraicIndependent_of_isSeparable
∀ {K : Type u_1} {L : Type u_2} {ι : Type u_3} [inst : Field L] [inst_1 : Field K] [inst_2 : Algebra K L] {v : ι → L},
AlgebraicIndependent K v →
∀ [Algebra.IsSeparable (↥(IntermediateField.adjoin K (Set.range v))) L], Algebra.FormallySmooth K LSeparably generated extensions are formally smooth.
- Defined in
- Mathlib.RingTheory.Smooth.Field
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.rangestatement and proof · cited by 4,705
- IntermediateFieldstatement · cited by 988
- IntermediateField.adjoinstatement and proof · cited by 382
- Algebra.IsSeparablestatement and proof · cited by 210
- AlgebraicIndependentstatement and proof · cited by 120
- Algebra.FormallySmoothstatement and proof · cited by 60
- Algebra.FormallyEtaleproof · cited by 37
- Algebra.FormallySmooth.compproof · cited by 9
- Algebra.FormallyEtale.of_isSeparableproof · cited by 3
- Algebra.FormallySmooth.adjoin_of_algebraicIndependentproof · cited by 2
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