Theorems · Definition · commutative algebra
ZMod.prodEquivPi
{ι : Type u_3} →
[inst : Fintype ι] →
(a : ι → ℕ) → Pairwise (Function.onFun Nat.Coprime a) → ZMod (∏ i, a i) ≃+* ((i : ι) → ZMod (a i))The Chinese remainder theorem, elementary version for ZMod. See also
Mathlib/Data/ZMod/Basic.lean for versions involving only two numbers.
- Defined in
- Mathlib.Data.ZMod.QuotientRing
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
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.
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- RingEquivstatement · cited by 1,147
- ZModstatement · cited by 1,024
- Ideal.spanproof · cited by 948
- Function.onFunstatement and proof · cited by 570
- RingEquiv.symmproof · cited by 567
- Pairwisestatement and proof · cited by 516
- IsCoprimeproof · cited by 321
- RingEquiv.transproof · cited by 54
- Ideal.quotEquivOfEqproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- ZMod.prodEquivPi_applystatement and proof · cited by 0
- ZMod.equivPiproof · cited by 0