Theorems · Definition · commutative algebra
Perfection.pthRoot
(R : Type u_1) →
[inst : CommSemiring R] →
(p : ℕ) → [hp : Fact (Nat.Prime p)] → [inst_1 : CharP R p] → Perfection R p →+* Perfection R pThe p-th root of an element of the perfection.
The preferred way to use this is (frobeniusEquiv (Perfection R p) p).symm.
- Defined in
- Mathlib.RingTheory.Perfection
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringFactCharP
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.
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- MonoidHomproof · cited by 3,629
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- CharPstatement and proof · cited by 478
- Perfectionstatement and proof · cited by 84
- Perfection.pthRootMonoidHomproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- Perfection.pthRoot_eq_symm_frobeniusEquivstatement and proof · cited by 2
- Perfection.pthRoot_frobeniusstatement · cited by 1
- Perfection.frobenius_pthRootstatement · cited by 0
- Perfection.pthRootMonoidHom_eq_pthRootstatement · cited by 0
- Perfection.coe_pthRoot_eq_symm_frobeniusEquivstatement · cited by 0