Theorems · Theorem · commutative algebra
FractionalIdeal.count_ne_zero
∀ {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] (v : IsDedekindDomain.HeightOneSpectrum R)
{I : FractionalIdeal (nonZeroDivisors R) K},
I ≠ 0 →
FractionalIdeal.count K v I =
↑((Associates.mk v.asIdeal).count (Associates.mk (Classical.choose ⋯)).factors) -
↑((Associates.mk v.asIdeal).count (Associates.mk (Ideal.span {Classical.choose ⋯})).factors)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Idealstatement · cited by 4,748
- Algebra.algebraMapstatement · cited by 4,706
- Ideal.spanstatement and proof · cited by 948
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
Cited by2
Results whose statement or proof uses this declaration.
- FractionalIdeal.finite_factorsproof · cited by 0
- FractionalIdeal.finprod_heightOneSpectrum_factorization'proof · cited by 0