Theorems · Theorem · commutative algebra
Submodule.torsionBySet_eq_torsionBySet_span
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (s : Set R),
Submodule.torsionBySet R M s = Submodule.torsionBySet R M ↑(Ideal.span s)Torsion by a set is torsion by the ideal generated by it.
- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement · cited by 7,192
- Set.Elemproof · cited by 7,166
- Idealstatement · cited by 4,748
- le_antisymmproof · cited by 2,068
- Ideal.spanstatement and proof · cited by 948
- Submodule.subset_spanproof · cited by 234
- Ideal.span_leproof · cited by 70
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.torsionBySet_span_singleton_eqproof · cited by 6
- Ideal.iSup_primaryComponent_eq_topproof · cited by 1