Theorems · Theorem · field theory
le_algebraicClosure_iff
∀ (F : Type u_1) (E : Type u_2) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (L : IntermediateField F E), L ≤ algebraicClosure F E ↔ Algebra.IsAlgebraic F ↥L
An intermediate field of E / F is contained in the algebraic closure of F in E
if and only if it is algebraic over F.
- Defined in
- Mathlib.FieldTheory.AlgebraicClosure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHom.idproof · cited by 18,349
- Algebrastatement and proof · cited by 11,388
- CommSemiringproof · cited by 10,911
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- IsScalarTowerproof · cited by 3,896
- IsDomainproof · cited by 2,196
- IntermediateFieldstatement and proof · cited by 988
- Polynomial.aevalproof · cited by 615
- Module.IsTorsionFreeproof · cited by 600
- Algebra.IsAlgebraicstatement and proof · cited by 322
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.isAlgebraic_adjoin_iff_isAlgebraicproof · cited by 0