algEquivGaloisField — Mathlib

English

As above, the finrank relations hold for GaloisField in repeated simplifications.

Русский

Как и ранее, размерности устойчивы в повторных леммах.

LaTeX

$$Module.finrank (ZMod p) (GaloisField p n) = n$$

Lean4

/-- Any finite field is (possibly noncanonically) isomorphic to some Galois field. -/
def algEquivGaloisField (h : Nat.card K = p ^ n) : K ≃ₐ[ZMod p] GaloisField p n :=
  haveI := FiniteField.isSplittingField_of_nat_card_eq _ _ h
  IsSplittingField.algEquiv _ _

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