Theorems · Theorem · number theory

IsPrimitiveRoot.autToPow_injective

∀ {n : ℕ} [inst : NeZero n] (K : Type u_1) [inst_1 : Field K] {L : Type u_2} {μ : L} [inst_2 : CommRing L]
  [inst_3 : IsDomain L] (hμ : IsPrimitiveRoot μ n) [inst_4 : Algebra K L] [IsCyclotomicExtension {n} K L],
  Function.Injective ⇑(IsPrimitiveRoot.autToPow K hμ)

IsPrimitiveRoot.autToPow is injective in the case that it's considered over a cyclotomic field extension.

Defined in

Mathlib.NumberTheory.Cyclotomic.Gal

Cited by

0 results in Mathlib

Foundations

Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NeZeroFieldCommRingIsDomainAlgebraIsCyclotomicExtension