Theorems · Theorem · commutative algebra
Ideal.sup_mul_inf
∀ {A : Type u_2} [inst : CommRing A] [IsDedekindDomain A] (I J : Ideal A), (I ⊔ J) * (I ⊓ J) = I * J- Cited by
- 1 results in Mathlib
- Foundations
- Depth 148 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.
Cites21
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
- IsDedekindDomainstatement and proof · cited by 668
- NormalizedGCDMonoidproof · cited by 159
- GCDMonoid.gcdproof · cited by 143
- GCDMonoid.lcmproof · cited by 78
- sup_le_iffproof · cited by 58
- le_inf_iffproof · cited by 48
- GCDMonoid.gcd_dvd_leftproof · cited by 36
- GCDMonoid.gcd_dvd_rightproof · cited by 34
- Ideal.dvd_iff_leproof · cited by 33
- associated_iff_eqproof · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.sup_mul_infproof · cited by 0