Theorems · Theorem · commutative algebra
FractionalIdeal.finite_factors
∀ {R : Type u_1} [inst : CommRing R] {K : Type u_2} [inst_1 : Field K] [inst_2 : Algebra R K]
[inst_3 : IsFractionRing R K] [inst_4 : IsDedekindDomain R] (I : FractionalIdeal (nonZeroDivisors R) K),
∀ᶠ (v : IsDedekindDomain.HeightOneSpectrum R) in Filter.cofinite, FractionalIdeal.count K v I = 0val_v(I) = 0 for all but finitely many maximal ideals of R.
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- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Algebrastatement and proof · cited by 11,388
- Filterproof · cited by 8,121
- Fieldstatement and proof · cited by 7,404
- Set.ofPredproof · cited by 6,101
- Filter.Eventuallystatement and proof · cited by 3,134
- Set.Finiteproof · cited by 1,814
- 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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