Theorems · Theorem · commutative algebra
Ideal.IsPrime.isPrimary
∀ {R : Type u_1} [inst : CommSemiring R] {I : Ideal R}, I.IsPrime → I.IsPrimary- Defined in
- Mathlib.RingTheory.Ideal.IsPrimary
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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.
- CommSemiringstatement and proof · cited by 10,911
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.IsPrime.ne_top'proof · cited by 38
- Ideal.IsPrime.mem_or_memproof · cited by 22
- Ideal.le_radicalproof · cited by 16
- Ideal.IsPrimarystatement · cited by 13
- Ideal.isPrimary_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalization.under_map_of_isPrime_disjointproof · cited by 15
- associatedPrimes.finiteproof · cited by 3