Theorems · Theorem · field theory
le_algebraicClosure
∀ (F : Type u_1) (E : Type u_2) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (L : IntermediateField F E) [Algebra.IsAlgebraic F ↥L], L ≤ algebraicClosure F E
An intermediate field of E / F is contained in the algebraic closure of F in E
if it is algebraic over F.
- Defined in
- Mathlib.FieldTheory.AlgebraicClosure
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- IntermediateFieldstatement and proof · cited by 988
- Algebra.IsAlgebraicstatement and proof · cited by 322
- Algebra.IsAlgebraic.isAlgebraicproof · cited by 51
- algebraicClosurestatement · cited by 22
- le_algebraicClosure'proof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- le_algebraicClosure_iffproof · cited by 1
- algebraicClosure.normalClosure_eq_selfproof · cited by 0