Theorems · Theorem · number theory
IsPrimitiveRoot.map_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], IsPrimitiveRoot ζ k → Function.Injective ⇑f → IsPrimitiveRoot (f ζ) k- Cited by
- 19 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- FunLikestatement and proof · cited by 2,560
- CommMonoidstatement and proof · cited by 2,264
- map_oneproof · cited by 861
- map_powproof · cited by 503
- IsPrimitiveRootstatement and proof · cited by 356
- MonoidHomClassstatement and proof · cited by 244
- IsPrimitiveRoot.pow_eq_oneproof · cited by 48
- orderOf_dvd_of_pow_eq_oneproof · cited by 24
- IsPrimitiveRoot.eq_orderOfproof · cited by 18
Cited by19
Results whose statement or proof uses this declaration.
- X_pow_sub_C_eq_prodproof · cited by 2
- NumberField.InfinitePlace.IsPrimitiveRoot.nrRealPlaces_eq_zero_of_two_ltproof · cited by 2
- Ideal.rootsOfUnityMapQuot_injectiveproof · cited by 2
- IsPrimitiveRoot.map_iff_of_injectiveproof · cited by 2
- IsCyclotomicExtension.Rat.associated_zeta_sub_one_pow_primeproof · cited by 1
- IsPrimitiveRoot.idealQuotient_mkproof · cited by 1
- autEquivRootsOfUnity_smulproof · cited by 1
- isSplittingField_X_pow_sub_C_of_root_adjoin_eq_topproof · cited by 1
- IsCyclotomicExtension.lcm_supproof · cited by 1
- IsCyclotomicExtension.le_of_dvdproof · cited by 1
- IsCyclotomicExtension.mem_of_pow_eq_oneproof · cited by 1
- IsCyclotomicExtension.nonempty_algEquiv_adjoin_of_isSepClosedproof · cited by 1