Theorems · Theorem · commutative algebra
IsDedekindDomain.HeightOneSpectrum.prime
∀ {R : Type u_1} [inst : CommRing R] [IsDedekindDomain R] (v : IsDedekindDomain.HeightOneSpectrum R), Prime v.asIdeal- Cited by
- 7 results in Mathlib
- Foundations
- Depth 147 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 · cited by 4,748
- IsDedekindDomainstatement and proof · cited by 668
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- Primestatement · cited by 277
- IsDedekindDomain.HeightOneSpectrum.asIdealstatement · cited by 156
- IsDedekindDomain.HeightOneSpectrum.ne_botproof · cited by 15
- Ideal.prime_of_isPrimeproof · cited by 15
Cited by7
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.irreducibleproof · cited by 13
- IsDedekindDomain.HeightOneSpectrum.intValuation_eq_exp_neg_multiplicityproof · cited by 2
- IsDedekindDomain.exists_sup_span_eqproof · cited by 2
- IsDedekindDomain.HeightOneSpectrum.emultiplicity_supproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.intValuation_liesOverproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.multiplicity_iSupproof · cited by 0
- IsDedekindDomain.HeightOneSpectrum.ofPrime_primestatement · cited by 0