Theorems · Theorem · field theory
IsPurelyInseparable.inseparable
∀ (F : Type u_1) {E : Type u_2} [inst : CommRing F] [inst_1 : Ring E] [inst_2 : Algebra F E] [IsPurelyInseparable F E]
(x : E), IsSeparable F x → x ∈ (algebraMap F E).range- Cited by
- 4 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapstatement · cited by 4,706
- Subringstatement · cited by 602
- RingHom.rangestatement · cited by 138
- IsPurelyInseparablestatement and proof · cited by 84
- IsSeparablestatement · cited by 68
- IsPurelyInseparable.inseparable'proof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- IsPurelyInseparable.surjective_algebraMap_of_isSeparableproof · cited by 6
- separableClosure.eq_bot_of_isPurelyInseparableproof · cited by 3
- IsPurelyInseparable.tower_botproof · cited by 1
- AlgEquiv.isPurelyInseparableproof · cited by 1