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Theorems · Theorem · number theory

IsPrimitiveRoot.map_iff_of_injective

∀ {M : Type u_1} {N : Type u_2} {F : Type u_6} [inst : CommMonoid M] [inst_1 : CommMonoid N] {k : ℕ} {ζ : M} {f : F}
  [inst_2 : FunLike F M N] [MonoidHomClass F M N],
  Function.Injective ⇑f → (IsPrimitiveRoot (f ζ) k ↔ IsPrimitiveRoot ζ k)
Defined in
Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots
Cited by
2 results in Mathlib
Foundations
Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommMonoidCommMonoidFunLikeMonoidHomClass
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Polynomial.isRoot_cyclotomic_iff · cited by 12Polynomial.isRoot_cycloto…IsPrimitiveRoot.coe_coe_iff · cited by 0IsPrimitiveRoot.coe_coe_i…DFunLike.coe · cited by 62936DFunLike.coeFunLike · cited by 2560FunLikeCommMonoid · cited by 2264CommMonoidIsPrimitiveRoot · cited by 356IsPrimitiveRootMonoidHomClass · cited by 244MonoidHomClassIsPrimitiveRoot.map_of_injective · cited by 19IsPrimitiveRoot.map_of_in…IsPrimitiveRoot.of_map_of_injective · cited by 2IsPrimitiveRoot.of_map_of…IsPrimitiveRoot.map_iff_of_in…CITED BYCITES

Cites7

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

Cited by2

Results whose statement or proof uses this declaration.