Theorems · Theorem · field theory
perfectField_of_isSeparable_of_perfectField_top
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [Algebra.IsSeparable F E] [PerfectField E], PerfectField F
If E / F is a separable extension, E is perfect, then F is also perfect.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.IsSeparablestatement and proof · cited by 210
- PerfectFieldstatement and proof · cited by 36
- perfectField_of_perfectClosure_eq_botproof · cited by 1
- perfectClosure.eq_bot_of_isSeparableproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- perfectField_iff_isSeparable_algebraicClosureproof · cited by 0