Theorems · Theorem · field theory
algebraicClosure.normalClosure_eq_self
∀ (F : Type u_1) (E : Type u_2) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E], IntermediateField.normalClosure F (↥(algebraicClosure F E)) E = algebraicClosure F E
The normal closure in E/F of the algebraic closure of F in E is equal to itself.
- Defined in
- Mathlib.FieldTheory.AlgebraicClosure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- AlgHomproof · cited by 3,236
- le_antisymmproof · cited by 2,068
- IntermediateFieldstatement · cited by 988
- AlgHom.fieldRangeproof · cited by 57
- IntermediateField.normalClosurestatement · cited by 38
- algebraicClosurestatement and proof · cited by 22
- IntermediateField.le_normalClosureproof · cited by 8
- normalClosure_le_iffproof · cited by 3
- le_algebraicClosureproof · cited by 2
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