Theorems · Theorem · commutative algebra
Submodule.iSup_torsionBy_eq_torsionBy_prod
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type u_3}
{S : Finset ι} {q : ι → R},
(↑S).Pairwise (Function.onFun IsCoprime q) →
⨆ i ∈ S, Submodule.torsionBy R M (q i) = Submodule.torsionBy R M (∏ i ∈ S, q i)- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
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- Modulestatement and proof · cited by 20,661
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Idealproof · cited by 4,748
- iSupstatement and proof · cited by 2,415
- Finset.prodstatement and proof · cited by 2,356
- Ideal.spanproof · cited by 948
- Function.onFunstatement and proof · cited by 570
- Set.Pairwisestatement and proof · cited by 321
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