Theorems · Definition · number theory
IsPrimitiveRoot.zmodEquivZPowers
{R : Type u_4} →
{k : ℕ} → [inst : CommRing R] → {ζ : Rˣ} → IsPrimitiveRoot ζ k → ZMod k ≃+ Additive ↥(Subgroup.zpowers ζ)The (additive) monoid equivalence between ZMod k
and the powers of a primitive root of unity ζ.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- AddEquivstatement · cited by 1,087
- ZModstatement and proof · cited by 1,024
- Additivestatement · cited by 356
- IsPrimitiveRootstatement and proof · cited by 356
- Subgroup.zpowersstatement · cited by 204
- AddMonoidHom.kerproof · cited by 158
- Additive.ofMulproof · cited by 155
- ZMod.castproof · cited by 87
Cited by10
Results whose statement or proof uses this declaration.
- autEquivZmodproof · cited by 5
- IsPrimitiveRoot.zmodEquivZPowers_apply_coe_intstatement · cited by 3
- IsPrimitiveRoot.zpowers_eqproof · cited by 3
- IsPrimitiveRoot.zmodEquivZPowers_apply_coe_natstatement and proof · cited by 1
- IsPrimitiveRoot.zmodEquivZPowers_symm_apply_powstatement and proof · cited by 1
- IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpowstatement and proof · cited by 1
- autEquivZmod_symm_apply_intCastproof · cited by 1
- IsPrimitiveRoot.zmodEquivZPowers_symm_apply_pow'statement · cited by 0
- IsPrimitiveRoot.zmodEquivZPowers_symm_apply_zpow'statement · cited by 0
- IsPrimitiveRoot.zmodEquivZPowers.congr_simpstatement and proof · cited by 0