Theorems · Theorem · commutative algebra
Ideal.primeCompl_le_nonZeroDivisors
∀ {R : Type u_1} [inst : CommSemiring R] [NoZeroDivisors R] (P : Ideal R) [inst_2 : P.IsPrime],
P.primeCompl ≤ nonZeroDivisors R- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Submonoidstatement · cited by 3,086
- nonZeroDivisorsstatement · cited by 895
- Ideal.IsPrimestatement and proof · cited by 827
- NoZeroDivisorsstatement and proof · cited by 545
- Ideal.primeComplstatement · cited by 462
- Ideal.zero_memproof · cited by 37
- le_nonZeroDivisors_of_noZeroDivisorsproof · cited by 5
Cited by17
Results whose statement or proof uses this declaration.
- Ideal.relNorm_algebraMapproof · cited by 4
- MaximalSpectrum.iInf_localization_eq_botstatement and proof · cited by 3
- Algebra.trace_quotient_eq_of_isDedekindDomainproof · cited by 3
- Ideal.IsDedekindDomain.ramificationIdx'_eq_one_iffproof · cited by 3
- IsIntegrallyClosed.of_localization_maximalproof · cited by 2
- Polynomial.not_weaklyQuasiFiniteAtproof · cited by 2
- IsLocalization.AtPrime.not_isFieldproof · cited by 2
- IsLocalization.isDomain_of_atPrimeproof · cited by 1
- IsIntegrallyClosed.of_localizationstatement and proof · cited by 1
- IsLocalization.AtPrime.isDedekindDomainproof · cited by 1
- Ideal.spanNorm_spanNormproof · cited by 1
- IsLocalization.OverPrime.mem_normalizedFactors_of_isPrimeproof · cited by 1