Theorems · Theorem · field theory
isPurelyInseparable_iff
∀ {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), IsIntegral F x ∧ (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.
Cites11
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 and proof · cited by 4,706
- Subringstatement · cited by 602
- IsIntegralstatement and proof · cited by 427
- RingHom.rangestatement and proof · cited by 138
- IsPurelyInseparablestatement and proof · cited by 84
- IsSeparablestatement and proof · cited by 68
- IsPurelyInseparable.inseparable'proof · cited by 4
- IsPurelyInseparable.isIntegral'proof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- isPurelyInseparable_iff_pow_memproof · cited by 10
- separableClosure.eq_bot_iffproof · cited by 1
- isPurelyInseparable_of_finSepDegree_eq_oneproof · cited by 1
- isPurelyInseparable_iff_fd_isPurelyInseparableproof · cited by 0