Theorems · Theorem · commutative algebra
Ideal.mul_eq_inf_of_coprime
∀ {R : Type u} [inst : CommSemiring R] {I J : Ideal R}, I ⊔ J = ⊤ → I * J = I ⊓ J- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 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.
Cites13
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
- SetLike.coeproof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- mul_oneproof · cited by 3,885
- le_antisymmproof · cited by 2,068
- mul_addproof · cited by 413
- Submodule.mem_supproof · cited by 73
- Ideal.eq_top_iff_oneproof · cited by 56
- Ideal.add_memproof · cited by 36
- Ideal.mul_mem_mulproof · cited by 29
- Ideal.mul_le_infproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.mul_eq_inf_of_isCoprimeproof · cited by 1
- Ideal.inf_eq_mul_of_isCoprimeproof · cited by 0