Theorems · Definition · field theory
PerfectClosure
(K : Type u) → [inst : CommRing K] → (p : ℕ) → [Fact (Nat.Prime p)] → [CharP K p] → Type u
The perfect closure is the smallest extension that makes frobenius surjective.
- Defined in
- Mathlib.FieldTheory.PerfectClosure
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- CharPstatement and proof · cited by 478
- PerfectClosure.Rproof · cited by 8
Cited by26
Results whose statement or proof uses this declaration.
- PerfectClosure.mkstatement · cited by 23
- PerfectClosure.mk_eq_iffstatement and proof · cited by 3
- PerfectClosure.liftOnstatement and proof · cited by 2
- PerfectClosure.natCaststatement and proof · cited by 2
- PerfectClosure.ofstatement · cited by 2
- PerfectClosure.frobenius_mkstatement · cited by 1
- PerfectClosure.mk_mul_mkstatement · cited by 1
- PerfectClosure.mk_powstatement and proof · cited by 1
- PerfectClosure.mk_succ_powstatement · cited by 1
- PerfectClosure.mk_zero_rightstatement and proof · cited by 1
- PerfectClosure.one_defstatement · cited by 1
- PerfectClosure.R.soundstatement and proof · cited by 1