Theorems · Theorem · field theory
isPurelyInseparable_iff_subsingleton_emb
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E], IsPurelyInseparable F E ↔ Subsingleton (Field.Emb F E)
An extension E / F is purely inseparable if and only there is at most one
embedding E →ₐ[F] AlgebraicClosure E
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 193 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
- IsPurelyInseparablestatement · cited by 84
- Nat.card_eq_one_iff_uniqueproof · cited by 15
- Field.Embstatement and proof · cited by 12
- isPurelyInseparable_iff_finSepDegree_eq_oneproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.tfae_universallyInjectiveproof · cited by 0