Theorems · Theorem · field theory
IsPurelyInseparable.pow_mem
∀ (F : Type u) {E : Type v} [inst : Field F] [inst_1 : Ring E] [IsDomain E] [inst_3 : Algebra F E] (q : ℕ) [ExpChar F q]
(x : E) [IsPurelyInseparable F E], ∃ n, x ^ q ^ n ∈ (algebraMap F E).range- Cited by
- 4 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- Subringstatement · cited by 602
- ExpCharstatement and proof · cited by 276
- RingHom.rangestatement · cited by 138
- IsPurelyInseparablestatement and proof · cited by 84
- isPurelyInseparable_iff_pow_memproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- IsPurelyInseparable.injective_comp_algebraMapproof · cited by 3
- Algebra.FormallyUnramified.range_eq_top_of_isPurelyInseparableproof · cited by 1
- IsPurelyInseparable.exists_pow_pow_mem_range_tensorProduct_of_expCharproof · cited by 1