Theorems · Theorem · commutative algebra
Module.isTorsionBySet_iff_torsionBySet_eq_top
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (s : Set R),
Module.IsTorsionBySet R M s ↔ Submodule.torsionBySet R M s = ⊤- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- eq_top_iffproof · cited by 236
- Submodule.torsionBySetstatement and proof · cited by 34
- Module.IsTorsionBySetstatement and proof · cited by 24
- Submodule.mem_torsionBySet_iffproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Submodule.torsionBySet_isInternalproof · cited by 2
- Module.isTorsionBy_iff_torsionBy_eq_topproof · cited by 2
- Submodule.torsionBySet_torsionBySet_eq_topproof · cited by 0