Theorems · Theorem · commutative algebra
Ideal.mul_mem_mul_rev
∀ {R : Type u} [inst : CommSemiring R] {I J : Ideal R} {r s : R}, r ∈ I → s ∈ J → s * r ∈ I * J- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 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.
Cites4
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
- mul_commproof · cited by 2,262
- Ideal.mul_mem_mulproof · cited by 29
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.mul_eq_inf_of_coprimeproof · cited by 2
- Ideal.mul_commproof · cited by 0