Theorems · Theorem · number theory

FiniteField.frobeniusAlgEquiv_apply

∀ (K : Type u_1) (R : Type u_2) [inst : Field K] [inst_1 : Fintype K] [inst_2 : CommRing R] [inst_3 : Algebra K R]
  (p : ℕ) [inst_4 : ExpChar R p] [inst_5 : PerfectRing R p] (a : R),
  (FiniteField.frobeniusAlgEquiv K R p) a = a ^ Fintype.card K

Defined in: Mathlib.FieldTheory.Finite.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Fintype CommRing Algebra ExpChar PerfectRing

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Fintypestatement and proof · cited by 7,736
Fieldstatement and proof · cited by 7,404
AlgEquivstatement · cited by 1,681
Fintype.cardstatement · cited by 1,386
ExpCharstatement and proof · cited by 276
PerfectRingstatement and proof · cited by 154
FiniteField.frobeniusAlgEquivstatement and proof · cited by 2

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