Theorems · Theorem · field theory
isPurelyInseparable_iff_finSepDegree_eq_one
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E], IsPurelyInseparable F E ↔ Field.finSepDegree F E = 1
An extension is purely inseparable if and only if it has finite separable degree one.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 192 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 and proof · cited by 84
- Field.finSepDegreestatement and proof · cited by 24
- IsPurelyInseparable.finSepDegree_eq_oneproof · cited by 2
- isPurelyInseparable_of_finSepDegree_eq_oneproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- isPurelyInseparable_iff_subsingleton_embproof · cited by 1
- IsPurelyInseparable.of_injective_comp_algebraMapproof · cited by 0