Theorems · Theorem · commutative algebra
Ideal.prime_of_isPrime
∀ {A : Type u_2} [inst : CommRing A] [IsDedekindDomain A] {P : Ideal A}, P ≠ ⊥ → P.IsPrime → Prime P- Cited by
- 15 results in Mathlib
- Foundations
- Depth 146 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.
Cites10
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
- Bot.botstatement and proof · cited by 4,720
- Ideal.IsPrimestatement and proof · cited by 827
- IsDedekindDomainstatement and proof · cited by 668
- Primestatement · cited by 277
- Ideal.IsPrime.ne_topproof · cited by 82
- Ideal.le_of_dvdproof · cited by 9
- Ideal.IsPrime.mul_leproof · cited by 8
- Ideal.isUnit_iffproof · cited by 7
Cited by15
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.primeproof · cited by 7
- Ideal.prime_iff_isPrimeproof · cited by 6
- Ideal.IsDedekindDomain.ramificationIdx'_eq_normalizedFactors_countproof · cited by 5
- Ideal.count_associates_factors_eqproof · cited by 4
- Ideal.IsDedekindDomain.ramificationIdx'_ne_zeroproof · cited by 3
- Ideal.IsDedekindDomain.ramificationIdx_eq_multiplicityproof · cited by 2
- Ideal.finprod_not_dvdproof · cited by 1
- Ideal.isPrime_iff_bot_or_primeproof · cited by 1
- Ideal.eq_prime_pow_of_succ_lt_of_leproof · cited by 1
- Ideal.mem_prime_of_mul_mem_powproof · cited by 1
- Ideal.exists_relNorm_eq_pow_of_isPrimeproof · cited by 1
- IsLocalization.OverPrime.mem_normalizedFactors_of_isPrimeproof · cited by 1