Theorems · Definition · commutative algebra
Ideal.quotientInfEquivQuotientProd
{R : Type u_2} → [inst : CommRing R] → (I J : Ideal R) → IsCoprime I J → R ⧸ I ⊓ J ≃+* (R ⧸ I) × R ⧸ JChinese remainder theorem, specialized to two ideals.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 92 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- RingEquivstatement · cited by 1,147
- Matrix.vecConsproof · cited by 852
- Matrix.vecEmptyproof · cited by 832
- Function.onFunproof · cited by 570
- Pairwiseproof · cited by 516
- IsCoprimestatement and proof · cited by 321
- RingEquiv.transproof · cited by 54
- Ideal.quotEquivOfEqproof · cited by 15
- Ideal.quotientInfRingEquivPiQuotientproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- Ideal.quotientMulEquivQuotientProdproof · cited by 8
- Ideal.quotientInfEquivQuotientProd_fststatement · cited by 0
- Ideal.snd_comp_quotientInfEquivQuotientProdstatement and proof · cited by 0
- Ideal.quotientInfEquivQuotientProd_sndstatement · cited by 0
- IsLocalRing.exists_surjective_of_not_isLocalRingproof · cited by 0
- Ideal.fst_comp_quotientInfEquivQuotientProdstatement and proof · cited by 0