Theorems · Definition · field theory

IsPerfectClosure.equiv

{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) →
              (j : K →+* M) →
                (p : ℕ) →
                  [inst_3 : ExpChar M p] →
                    [ExpChar K p] →
                      [inst_5 : ExpChar L p] →
                        [inst_6 : PerfectRing L p] →
                          [IsPerfectClosure i p] → [inst_8 : PerfectRing M p] → [IsPerfectClosure j p] → L ≃+* M

If L and M are both perfect closures of K, then there is a ring isomorphism L ≃+* M. This is similar to IsAlgClosure.equiv and IsSepClosure.equiv.

Defined in

Mathlib.FieldTheory.IsPerfectClosure

Cited by

13 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingExpCharExpCharExpCharPerfectRingIsPerfectClosurePerfectRingIsPerfectClosure