Theorems · Definition · field theory

PerfectRing.lift

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

If i : K →+* L and j : K →+* M are ring homomorphisms of characteristic p rings, such that i is p-radical, and M is a perfect ring, then PerfectRing.liftAux is a ring homomorphism. This is similar to IsAlgClosed.lift and IsSepClosed.lift.

Defined in

Mathlib.FieldTheory.IsPerfectClosure

Cited by

19 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingExpCharExpCharPerfectRingIsPRadicalExpChar