Theorems · Definition · commutative algebra
Submodule.torsionBySet
(R : Type u_1) → (M : Type u_2) → [inst : CommSemiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → Set R → Submodule R M
The submodule containing all elements x of M such that a • x = 0 for all a in s.
- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Submodulestatement · cited by 7,192
- Set.imageproof · cited by 5,609
- InfSet.sInfproof · cited by 935
- Submodule.torsionByproof · cited by 31
Cited by35
Results whose statement or proof uses this declaration.
- Ideal.primaryComponentproof · cited by 10
- Submodule.torsionBySet_span_singleton_eqstatement · cited by 6
- Submodule.torsionBySet_le_torsionBySet_of_subsetstatement · cited by 5
- Submodule.torsionBySet_singleton_eqstatement · cited by 5
- Submodule.mem_torsionBySet_iffstatement and proof · cited by 5
- Submodule.iSup_torsionBySet_ideal_eq_torsionBySet_iInfstatement and proof · cited by 5
- Submodule.supIndep_torsionBySet_idealstatement and proof · cited by 4
- Module.isTorsionBySet_iff_torsionBySet_eq_topstatement and proof · cited by 3
- Submodule.isInternal_prime_power_torsionstatement · cited by 2
- Submodule.torsionBySet_eq_torsionBySet_spanstatement and proof · cited by 2
- Submodule.torsionBySet_isInternalstatement and proof · cited by 2
- Submodule.torsionBySet_univstatement and proof · cited by 2