Theorems · Theorem · field theory
IsAlgClosed.isAlgClosure_of_transcendence_basis
∀ {R : Type u_1} {K : Type u_3} [inst : CommRing R] [inst_1 : Field K] [inst_2 : Algebra R K] {ι : Type u_4} (v : ι → K)
[IsAlgClosed K], IsTranscendenceBasis R v → IsAlgClosure (↥(Algebra.adjoin R (Set.range v))) K- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Fieldstatement and proof · cited by 7,404
- Set.rangestatement · cited by 4,705
- Subalgebrastatement · cited by 1,353
- Algebra.adjoinstatement · cited by 535
- IsAlgClosedstatement and proof · cited by 150
- IsTranscendenceBasisstatement and proof · cited by 74
- IsAlgClosurestatement · cited by 16
- IsTranscendenceBasis.isAlgebraicproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- IsAlgClosed.cardinal_le_max_transcendence_basisproof · cited by 2