Theorems · Definition · number theory
PadicInt.residueField
{p : ℕ} → [hp_prime : Fact (Nat.Prime p)] → IsLocalRing.ResidueField ℤ_[p] ≃+* ZMod pThe equivalence between the residue field of the p-adic integers and ℤ/pℤ
- Defined in
- Mathlib.NumberTheory.Padics.RingHoms
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fact
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- RingEquivstatement · cited by 1,147
- ZModstatement · cited by 1,024
- PadicIntstatement · cited by 179
- IsLocalRing.ResidueFieldstatement · cited by 156
- RingEquiv.transproof · cited by 54
- Ideal.quotEquivOfEqproof · cited by 15
- RingHom.quotientKerEquivOfSurjectiveproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- PadicInt.toZMod_eq_residueField_comp_residuestatement · cited by 0