Theorems · Theorem · field theory
isPurelyInseparable_iff_perfectClosure_eq_top
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E],
IsPurelyInseparable F E ↔ perfectClosure F E = ⊤A field extension E / F is purely inseparable if and only if the relative perfect closure of
F in E is equal to E.
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- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
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- Algebrastatement and proof · cited by 11,388
- Top.topstatement and proof · cited by 9,680
- Fieldstatement and proof · cited by 7,404
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- IntermediateFieldstatement · cited by 988
- Eq.geproof · cited by 375
- RingHom.rangeproof · cited by 138
- top_uniqueproof · cited by 102
- IsPurelyInseparablestatement · cited by 84
- ringExpCharproof · cited by 27
- perfectClosurestatement and proof · cited by 14
- isPurelyInseparable_iff_pow_memproof · cited by 10
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