Theorems · Definition · field theory

PerfectRing.liftEquiv

{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) →
              (p : ℕ) →
                [ExpChar M p] →
                  [ExpChar K p] → [PerfectRing M p] → [IsPRadical i p] → [ExpChar L p] → (K →+* M) ≃ (L →+* M)

If i : K →+* L is a homomorphism of characteristic p rings, such that i is p-radical, and M is a perfect ring of characteristic p, then K →+* M is in one-to-one correspondence with L →+* M, given by PerfectRing.lift. This generalizes PerfectClosure.lift.

Defined in

Mathlib.FieldTheory.IsPerfectClosure

Cited by

6 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingExpCharExpCharPerfectRingIsPRadicalExpChar