Theorems · Theorem · commutative algebra
Ideal.sup_eq_prod_inf_factors
∀ {T : Type u_4} [inst : CommRing T] [inst_1 : IsDedekindDomain T] {I J : Ideal T},
I ≠ ⊥ →
J ≠ ⊥ → I ⊔ J = (UniqueFactorizationMonoid.normalizedFactors I ∩ UniqueFactorizationMonoid.normalizedFactors J).prod- Cited by
- 3 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDedekindDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- Bot.botstatement and proof · cited by 4,720
- Multisetstatement and proof · cited by 2,627
- le_antisymmproof · cited by 2,068
- IsDedekindDomainstatement and proof · cited by 668
- Multiset.prodstatement and proof · cited by 528
- Multiset.countproof · cited by 302
- inf_le_leftproof · cited by 286
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- inf_le_rightproof · cited by 238
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.irreducible_pow_supproof · cited by 5
- IsDedekindDomain.HeightOneSpectrum.multiplicity_supproof · cited by 1
- sup_eq_prod_inf_factorsproof · cited by 0