Theorems · Theorem · field theory
mem_perfectClosure_iff_pow_mem
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (q : ℕ) [ExpChar F q] {x : E},
x ∈ perfectClosure F E ↔ ∃ n, x ^ q ^ n ∈ (algebraMap F E).range- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 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
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement and proof · cited by 4,706
- IntermediateFieldstatement · cited by 988
- Subringstatement · cited by 602
- ExpCharstatement and proof · cited by 276
- RingHom.rangestatement and proof · cited by 138
- ringExpChar.eqproof · cited by 15
- perfectClosurestatement · cited by 14
- mem_perfectClosure_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.isPurelyInseparable_adjoin_iff_pow_memproof · cited by 1
- IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_memproof · cited by 1