Theorems · Theorem · field theory
PerfectRing.ofSurjective
∀ (R : Type u_2) (p : ℕ) [inst : CommRing R] [inst_1 : ExpChar R p] [IsReduced R], Function.Surjective ⇑(frobenius R p) → PerfectRing R p
For a reduced ring, surjectivity of the Frobenius map is a sufficient condition for perfection.
- Defined in
- Mathlib.FieldTheory.Perfect
- 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- ExpCharstatement and proof · cited by 276
- PerfectRingstatement · cited by 154
- IsReducedstatement and proof · cited by 98
- frobeniusstatement and proof · cited by 80
- frobenius_injproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- perfectField_of_perfectClosure_eq_botproof · cited by 1
- perfectField_iff_splits_of_natSepDegree_eq_oneproof · cited by 1