Theorems · Theorem · field theory

PerfectRing.liftAux_apply

∀ {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 : PerfectRing M p]
  [inst_6 : IsPRadical i p] (x : L) (n : ℕ) (y : K),
  i y = x ^ p ^ n → PerfectRing.liftAux i j p x = (iterateFrobeniusEquiv M p n).symm (j y)

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 well-defined.

Defined in

Mathlib.FieldTheory.IsPerfectClosure

Cited by

2 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingExpCharExpCharPerfectRingIsPRadical