Theorems · Definition · commutative algebra
Ideal.quotientMulEquivQuotientProd
{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
- 8 results in Mathlib
- Foundations
- Depth 93 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.
Cites8
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 · cited by 2,301
- RingEquivstatement · cited by 1,147
- IsCoprimestatement and proof · cited by 321
- RingEquiv.transproof · cited by 54
- Ideal.quotEquivOfEqproof · cited by 15
- Ideal.quotientInfEquivQuotientProdproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- Ideal.quotientMulEquivQuotientProd_sndstatement · cited by 2
- not_dvd_differentIdeal_of_isCoprime_of_isSeparableproof · cited by 2
- dvd_differentIdeal_of_not_isSeparableproof · cited by 1
- cardQuot_mul_of_coprimeproof · cited by 1
- Ideal.snd_comp_quotientMulEquivQuotientProdstatement and proof · cited by 0
- Ideal.quotientMulEquivQuotientProd.congr_simpstatement and proof · cited by 0
- Ideal.fst_comp_quotientMulEquivQuotientProdstatement and proof · cited by 0
- Ideal.quotientMulEquivQuotientProd_fststatement · cited by 0