Theorems · Theorem · commutative algebra
Ideal.isPrime_nat_iff
∀ {P : Ideal ℕ}, P.IsPrime ↔ P = ⊥ ∨ P = IsLocalRing.maximalIdeal ℕ ∨ ∃ p, Nat.Prime p ∧ P = Ideal.span {p}- Defined in
- Mathlib.RingTheory.Ideal.NatInt
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- LT.lt.leproof · cited by 2,189
- Nat.Primestatement and proof · cited by 2,059
- eq_or_neproof · cited by 1,117
- Ideal.spanstatement and proof · cited by 948
- Ideal.IsPrimestatement and proof · cited by 827
- LE.le.antisymmproof · cited by 507
- Iff.notproof · cited by 489
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- AddMemClass.add_memproof · cited by 229
Cited by1
Results whose statement or proof uses this declaration.
- ringKrullDim_natproof · cited by 0