Theorems · Theorem · number theory
IsPrimitiveRoot.embeddingsEquivPrimitiveRoots.congr_simp
∀ {n : ℕ} [inst : NeZero n] {K : Type u} {L : Type v} [inst_1 : Field K] [inst_2 : CommRing L] [inst_3 : IsDomain L]
[inst_4 : Algebra K L] [inst_5 : IsCyclotomicExtension {n} K L] {ζ ζ_1 : L} (e_ζ : ζ = ζ_1) (hζ : IsPrimitiveRoot ζ n)
(C : Type u_1) [inst_6 : CommRing C] [inst_7 : IsDomain C] [inst_8 : Algebra K C]
(hirr : Irreducible (Polynomial.cyclotomic n K)),
hζ.embeddingsEquivPrimitiveRoots C hirr = ⋯.embeddingsEquivPrimitiveRoots C hirr- Cited by
- 0 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Finsetstatement · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- Equivstatement · cited by 8,337
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- AlgHomstatement · cited by 3,236
- IsDomainstatement and proof · cited by 2,196
- Irreduciblestatement and proof · cited by 496
- IsPrimitiveRootstatement and proof · cited by 356
- IsCyclotomicExtensionstatement and proof · cited by 220
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