Theorems · Definition · field theory

PerfectRing.liftAux

{K : Type u_1} →
  {L : Type u_2} →
    {M : Type u_3} →
      [inst : CommSemiring K] →
        [inst_1 : CommSemiring L] →
          [inst_2 : CommSemiring M] →
            (i : K →+* L) → (K →+* M) → (p : ℕ) → [ExpChar M p] → [PerfectRing M p] → [IsPRadical i p] → L → M

If i : K →+* L and j : K →+* M are ring homomorphisms of characteristic p rings, such that i is p-radical (in fact only the IsPRadical.pow_mem is required) and M is a perfect ring, then one can define a map L → M which maps an element x of L to y ^ (p ^ -n) if x ^ (p ^ n) is equal to some element y of K.

Defined in

Mathlib.FieldTheory.IsPerfectClosure

Cited by

6 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringCommSemiringExpCharPerfectRingIsPRadical