Theorems · Definition · commutative algebra
IsDedekindDomain.HeightOneSpectrum.maxPowDividing
{R : Type u_1} → [inst : CommRing R] → [IsDedekindDomain R] → IsDedekindDomain.HeightOneSpectrum R → Ideal R → Ideal RGiven a maximal ideal v and an ideal I of R, maxPowDividing returns the maximal
power of v dividing I.
- Cited by
- 17 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.
Cites8
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
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- IsDedekindDomain.HeightOneSpectrum.asIdealproof · cited by 156
- Associates.mkproof · cited by 137
- Associates.factorsproof · cited by 97
- Associates.countproof · cited by 79
Cited by17
Results whose statement or proof uses this declaration.
- Ideal.hasFiniteMulSupportstatement and proof · cited by 7
- Ideal.finprod_heightOneSpectrum_factorizationstatement and proof · cited by 6
- NumberField.HeightOneSpectrum.embedding_mul_absNormstatement · cited by 3
- Ideal.map_algebraMap_eq_finsetProd_powproof · cited by 2
- Associates.finprod_ne_zerostatement and proof · cited by 2
- IsDedekindDomain.HeightOneSpectrum.maxPowDividing_eq_pow_multiplicitystatement · cited by 2
- IsDedekindDomain.HeightOneSpectrum.maxPowDividing_eq_pow_multiset_countstatement · cited by 2
- Ideal.finprod_not_dvdstatement and proof · cited by 1
- Ideal.iInf_maxPowDividing_eqstatement and proof · cited by 1
- Ideal.iSup_primaryComponent_eq_topproof · cited by 1
- NumberField.FinitePlace.prod_eq_inv_abs_norm_intproof · cited by 1
- IsDedekindDomain.isOpen_of_ne_botproof · cited by 1