Theorems · Definition · number theory
ZMod.castHom
{n m : ℕ} → m ∣ n → (R : Type u_2) → [inst : Ring R] → [CharP R m] → ZMod n →+* RThe canonical ring homomorphism from ZMod n to a ring of characteristic dividing n.
See also ZMod.lift for a generalized version working in AddGroups.
- Defined in
- Mathlib.Data.ZMod.Basic
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- ZModstatement · cited by 1,024
- CharPstatement and proof · cited by 478
- ZMod.castproof · cited by 87
- ZMod.cast_addproof · cited by 3
- ZMod.cast_mulproof · cited by 3
- ZMod.cast_oneproof · cited by 2
Cited by63
Results whose statement or proof uses this declaration.
- ZMod.unitsMapproof · cited by 24
- FiniteField.cardproof · cited by 10
- PadicInt.limNthHomstatement and proof · cited by 8
- ZMod.unitsMap_surjectiveproof · cited by 7
- ZMod.chineseRemainderproof · cited by 6
- PadicInt.liftstatement and proof · cited by 6
- ZMod.cast_natCastproof · cited by 5
- PadicInt.nthHomSeqstatement and proof · cited by 4
- ZMod.cast_intCastproof · cited by 4
- PadicInt.zmod_cast_comp_toZModPowstatement and proof · cited by 4
- PadicInt.isCauSeq_nthHomstatement and proof · cited by 3
- PadicInt.lift_specstatement and proof · cited by 3