Theorems · Theorem · number theory
map_rootsOfUnity_eq_pow_self
∀ {R : Type u_4} {F : Type u_6} {k : ℕ} [NeZero k] [inst : CommRing R] [IsDomain R] [inst_2 : FunLike F R R]
[MonoidHomClass F R R] (σ : F) (ζ : ↥(rootsOfUnity k R)), ∃ m, σ ↑↑ζ = ↑↑ζ ^ m- Defined in
- Mathlib.RingTheory.RootsOfUnity.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- CommRingstatement and proof · cited by 17,173
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- FunLikestatement and proof · cited by 2,560
- IsDomainstatement and proof · cited by 2,196
- Units.valstatement and proof · cited by 1,966
- orderOfproof · cited by 324
- zpow_natCastproof · cited by 271
- MonoidHomClassstatement and proof · cited by 244
- pos_iff_ne_zeroproof · cited by 180
- rootsOfUnitystatement and proof · cited by 118
Cited by3
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.autToPow_specproof · cited by 5
- IsPrimitiveRoot.coe_autToPow_applystatement · cited by 1
- gal_X_pow_sub_one_isSolvableproof · cited by 1