Theorems · Theorem · field theory
Algebra.IsAlgebraic.isSepClosed
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [Algebra.IsAlgebraic F E]
[IsSepClosed F], IsSepClosed EIf E / F is an algebraic extension, F is separably closed,
then E is also separably closed.
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- 0 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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
- Algebra.IsAlgebraicstatement and proof · cited by 322
- AlgebraicClosureproof · cited by 53
- IsSepClosedstatement and proof · cited by 41
- Algebra.IsAlgebraic.transproof · cited by 12
- IsPurelyInseparable.tower_topproof · cited by 3
- isSepClosed_iff_isPurelyInseparable_algebraicClosureproof · cited by 1
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