Theorems · Theorem · field theory
IsAlgClosed.algebraicClosure_eq_bot_iff
∀ (F : Type u_1) (E : Type u_2) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [IsAlgClosed E], algebraicClosure F E = ⊥ ↔ IsAlgClosed F
If E / F is a field extension and E is algebraically closed, then the algebraic closure
of F in E is equal to F if and only if F is algebraically closed.
- Defined in
- Mathlib.FieldTheory.AlgebraicClosure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldFieldAlgebraIsAlgClosed
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Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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