Theorems · Theorem · commutative algebra
Ideal.isCoprime_iff_codisjoint
∀ {R : Type u} [inst : CommSemiring R] {I J : Ideal R}, IsCoprime I J ↔ Codisjoint I J- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 78 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.
Cites14
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.topproof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- LE.le.transproof · cited by 3,151
- IsCoprimestatement · cited by 321
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- Codisjointstatement and proof · cited by 197
- sup_leproof · cited by 159
- Ideal.one_eq_topproof · cited by 83
- Ideal.eq_top_iff_oneproof · cited by 56
- codisjoint_iffproof · cited by 53
Cited by6
Results whose statement or proof uses this declaration.
- Ideal.isCoprime_iff_sup_eqproof · cited by 10
- Ideal.isCoprime_of_isMaximalproof · cited by 3
- Ideal.isCoprime_iff_addproof · cited by 3
- Ideal.isCoprime_iff_gcdproof · cited by 2
- Ideal.isCoprime_tfaeproof · cited by 0
- IsCoprime.codisjointproof · cited by 0