Theorems · Theorem · commutative algebra
FractionalIdeal.sup_mul_inf
∀ {A : Type u_2} {K : Type u_3} [inst : CommRing A] [inst_1 : Field K] [IsDedekindDomain A] [inst_3 : Algebra A K]
[IsFractionRing A K] (I J : FractionalIdeal (nonZeroDivisors A) K), (I ⊓ J) * (I ⊔ J) = I * J- Cited by
- 0 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Idealproof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- map_mulproof · cited by 1,137
- Ideal.spanproof · cited by 948
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
- FractionalIdealstatement and proof · cited by 423
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