Theorems · Theorem · commutative algebra
Ideal.mul_eq_inf_of_isCoprime
∀ {R : Type u} [inst : CommSemiring R] {I J : Ideal R}, IsCoprime I J → I * J = I ⊓ J- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 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
- IsCoprime.sup_eqproof · cited by 6
- Ideal.mul_eq_inf_of_coprimeproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.prod_eq_iInf_of_pairwise_isCoprimeproof · cited by 4