Theorems · Theorem · commutative algebra
IsDedekindDomain.HeightOneSpectrum.emultiplicity_sup
∀ {R : Type u_3} [inst : CommRing R] [IsDedekindDomain R] (p : IsDedekindDomain.HeightOneSpectrum R) (I J : Ideal R),
emultiplicity p.asIdeal (I ⊔ J) = min (emultiplicity p.asIdeal I) (emultiplicity p.asIdeal J)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 154 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.
Cites20
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
- ENatstatement and proof · cited by 4,985
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- eq_or_neproof · cited by 1,117
- IsDedekindDomainstatement and proof · cited by 668
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- sup_of_le_leftproof · cited by 218
- inf_of_le_leftproof · cited by 186
- IsDedekindDomain.HeightOneSpectrum.asIdealstatement and proof · cited by 156
- emultiplicitystatement and proof · cited by 156
- sup_of_le_rightproof · cited by 143
Cited by1
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.emultiplicity_iSupproof · cited by 1