Theorems · Theorem · field theory
mem_perfectClosure_iff
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {x : E},
x ∈ perfectClosure F E ↔ ∃ n, x ^ ringExpChar F ^ n ∈ (algebraMap F E).range- Cited by
- 2 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 · cited by 4,706
- IntermediateFieldstatement · cited by 988
- Subringstatement · cited by 602
- RingHom.rangestatement · cited by 138
- ringExpCharstatement · cited by 27
- perfectClosurestatement · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- mem_perfectClosure_iff_pow_memproof · cited by 2
- mem_perfectClosure_iff_natSepDegree_eq_oneproof · cited by 1