Theorems · Theorem · commutative algebra
Ideal.isPrime_of_prime
∀ {A : Type u_2} [inst : CommRing A] [IsDedekindDomain A] {P : Ideal A}, Prime P → P.IsPrime- Cited by
- 17 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.
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
- Top.topproof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement · cited by 827
- IsDedekindDomainstatement and proof · cited by 668
- Primestatement and proof · cited by 277
- Ideal.one_eq_topproof · cited by 83
- isUnit_oneproof · cited by 48
- Prime.not_isUnitproof · cited by 29
- Prime.dvd_or_dvdproof · cited by 17
Cited by18
Results whose statement or proof uses this declaration.
- Ideal.prime_iff_isPrimeproof · cited by 6
- Ideal.finprod_heightOneSpectrum_factorizationproof · cited by 6
- IsDedekindDomain.HeightOneSpectrum.ofPrimeproof · cited by 4
- Ideal.eq_prime_pow_mul_coprimeproof · cited by 3
- IsDedekindDomain.inf_pow_eq_prod_of_primeproof · cited by 3
- Ideal.IsDedekindDomain.ramificationIdx_eq_factors_countproof · cited by 2
- Ideal.exists_isMaximal_dvd_of_dvd_absNormproof · cited by 2
- Ideal.isPrime_iff_bot_or_primeproof · cited by 1
- Ideal.isPrime_of_irreducible_absNormproof · cited by 1
- Submodule.exists_isInternal_prime_power_torsion_of_pidproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.mem_integers_of_valuation_le_oneproof · cited by 1