Theorems · Theorem · commutative algebra
Ring.DimensionLeOne.prime_le_prime_iff_eq
∀ {R : Type u_1} [inst : CommRing R] [Ring.DimensionLEOne R] {P Q : Ideal R} [hP : P.IsPrime] [hQ : Q.IsPrime],
P ≠ ⊥ → (P ≤ Q ↔ P = Q)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, 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.
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- Ideal.IsPrimestatement and proof · cited by 827
- Eq.leproof · cited by 605
- Ideal.IsPrime.ne_topproof · cited by 82
- Ideal.IsMaximal.eq_of_leproof · cited by 39
- Ideal.IsPrime.isMaximalproof · cited by 24
- Ring.DimensionLEOnestatement and proof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- IsPrincipalIdealRing.of_isDedekindDomain_of_uniqueFactorizationMonoidproof · cited by 0