Theorems · Theorem · field theory
isPurelyInseparable_iff_fd_isPurelyInseparable
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [Algebra.IsAlgebraic F E],
IsPurelyInseparable F E ↔ ∀ (L : IntermediateField F E), FiniteDimensional F ↥L → IsPurelyInseparable F ↥LAn algebraic extension is purely inseparable if and only if all of its finite-dimensional subextensions are purely inseparable.
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- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
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- Algebra.algebraMapproof · cited by 4,706
- FiniteDimensionalstatement and proof · cited by 1,854
- IntermediateFieldstatement and proof · cited by 988
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- IsIntegralproof · cited by 427
- IntermediateField.adjoinproof · cited by 382
- Algebra.IsAlgebraicstatement and proof · cited by 322
- Polynomial.Separableproof · cited by 117
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