Theorems · Theorem · commutative algebra
FractionalIdeal.count_coe
∀ {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) {J : Ideal R},
J ≠ 0 → FractionalIdeal.count K v ↑J = ↑((Associates.mk v.asIdeal).count (Associates.mk J).factors)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
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
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- one_mulproof · cited by 2,841
- nonZeroDivisorsstatement and proof · cited by 895
- map_oneproof · cited by 861
- IsFractionRingstatement and proof · cited by 738
- IsDedekindDomainstatement and proof · cited by 668
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.count_coe_nonnegproof · cited by 1