Theorems · Theorem · commutative algebra
Ideal.isPrime_int_iff
∀ {P : Ideal ℤ}, P.IsPrime ↔ P = ⊥ ∨ ∃ p, Nat.Prime p ∧ P = Ideal.span {↑p}- Defined in
- Mathlib.RingTheory.Ideal.NatInt
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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 · cited by 4,720
- Nat.Primestatement and proof · cited by 2,059
- Ideal.spanstatement and proof · cited by 948
- Ideal.IsPrimestatement · cited by 827
- Primeproof · cited by 277
- Nat.prime_iff_prime_intproof · cited by 27
- Int.prime_iff_natAbs_primeproof · cited by 11
- Ideal.isPrime_iff_of_isPrincipalIdealRing_of_noZeroDivisorsproof · cited by 1
- Int.span_natAbsproof · cited by 1
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