Theorems · Theorem · field theory
Algebra.FormallySmooth.adjoin_of_algebraicIndependent
∀ {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.FormallySmooth K ↥(IntermediateField.adjoin K (Set.range v))- Defined in
- Mathlib.RingTheory.Smooth.Field
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- nonZeroDivisorsproof · cited by 895
- Algebra.adjoinproof · cited by 535
- IntermediateField.adjoinstatement and proof · cited by 382
- AlgebraicIndependentstatement and proof · cited by 120
- Algebra.FormallySmoothstatement and proof · cited by 60
- AlgebraicIndependent.aevalEquivproof · cited by 17
- Algebra.FormallySmooth.compproof · cited by 9
- Algebra.FormallySmooth.of_equivproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.FormallySmooth.of_algebraicIndependent_of_isSeparableproof · cited by 0
- Algebra.FormallySmooth.of_algebraicIndependentproof · cited by 0