Theorems · Definition · commutative algebra

PerfectionMap.equiv

{p : ℕ} →
  [inst : Fact (Nat.Prime p)] →
    {R : Type u₁} →
      [inst_1 : CommSemiring R] →
        [inst_2 : CharP R p] →
          {P : Type u₃} →
            [inst_3 : CommSemiring P] →
              [inst_4 : CharP P p] →
                [inst_5 : PerfectRing P p] → {π : P →+* R} → PerfectionMap p π → P ≃+* Perfection R p

A perfection map induces an isomorphism to the perfection.

Defined in

Mathlib.RingTheory.Perfection

Cited by

7 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FactCommSemiringCharPCommSemiringCharPPerfectRing