Theorems · Theorem · commutative algebra
Ideal.isCoprime_iff_add
∀ {R : Type u} [inst : CommSemiring R] {I J : Ideal R}, IsCoprime I J ↔ I + J = 1- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 3 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.
Cites8
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
- IsCoprimestatement · cited by 321
- Ideal.one_eq_topproof · cited by 83
- codisjoint_iffproof · cited by 53
- Ideal.add_eq_supproof · cited by 7
- Ideal.isCoprime_iff_codisjointproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.isCoprime_iff_existsproof · cited by 4
- Ideal.isCoprime_tfaeproof · cited by 0
- IsCoprime.add_eqproof · cited by 0