Theorems · Theorem · commutative algebra
Ideal.prod_eq_iInf_of_pairwise_isCoprime
∀ {R : Type u} {ι : Type u_1} [inst : CommSemiring R] {s : Finset ι} {J : ι → Ideal R},
(↑s).Pairwise (Function.onFun IsCoprime J) → ∏ i ∈ s, J i = ⨅ i ∈ s, J i- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Top.topproof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Finset.prodstatement and proof · cited by 2,356
- iInfstatement and proof · cited by 1,690
- Function.onFunstatement and proof · cited by 570
- IsCoprimestatement and proof · cited by 321
- Set.Pairwisestatement and proof · cited by 321
- iInf_congr_Propproof · cited by 218
- Finset.coe_insertproof · cited by 124
Cited by4
Results whose statement or proof uses this declaration.
- IsArtinianRing.nilradical_pow_eq_iInfproof · cited by 3
- IsDedekindDomain.inf_pow_eq_prod_of_primeproof · cited by 3
- Ideal.iInf_maxPowDividing_eqproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.inf_pow_eq_prodproof · cited by 0