Theorems · Theorem · commutative algebra
Ideal.isCoprime_iff_sup_eq
∀ {R : Type u} [inst : CommSemiring R] {I J : Ideal R}, IsCoprime I J ↔ I ⊔ J = ⊤- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 79 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.
Cites6
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
- Top.topstatement and proof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- IsCoprimestatement · cited by 321
- codisjoint_iffproof · cited by 53
- Ideal.isCoprime_iff_codisjointproof · cited by 6
Cited by10
Results whose statement or proof uses this declaration.
- IsCoprime.sup_eqproof · cited by 6
- IsRelPrime.isCoprimeproof · cited by 5
- IsDedekindDomain.HeightOneSpectrum.isCoprime_pow_of_neproof · cited by 4
- IsDedekindDomain.inf_pow_eq_prod_of_primeproof · cited by 3
- IsDedekindDomain.HeightOneSpectrum.isCoprime_of_neproof · cited by 1
- MaximalSpectrum.isCoprime_of_neproof · cited by 1
- not_dvd_differentIdeal_iffproof · cited by 1
- Ideal.isCoprime_tfaeproof · cited by 0
- Ideal.coprime_of_no_prime_geproof · cited by 0
- cardQuot_mulproof · cited by 0