Theorems · Theorem · commutative algebra
Ideal.isCoprime_iff_exists
∀ {R : Type u} [inst : CommSemiring R] {I J : Ideal R}, IsCoprime I J ↔ ∃ i ∈ I, ∃ j ∈ J, i + j = 1- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 80 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.
Cites5
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
- Idealstatement and proof · cited by 4,748
- IsCoprimestatement and proof · cited by 321
- Ideal.isCoprime_iff_addproof · cited by 3
- Ideal.add_eq_one_iffproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.quotientInfToPiQuotient_surjproof · cited by 2
- NumberField.isCoprime_differentIdeal_of_isCoprime_discrproof · cited by 1
- Ideal.isCoprime_tfaeproof · cited by 0
- IsCoprime.existsproof · cited by 0