Theorems · Theorem · commutative algebra
Submodule.torsionBySet_span_singleton_eq
∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] (a : R),
Submodule.torsionBySet R M ↑(R ∙ a) = Submodule.torsionBy R M a- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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 · cited by 8,199
- Submodulestatement · cited by 7,192
- Submodule.spanstatement · cited by 1,504
- Submodule.torsionBySetstatement · cited by 34
- Submodule.torsionBystatement · cited by 31
- Submodule.torsionBySet_singleton_eqproof · cited by 5
- Submodule.torsionBySet_eq_torsionBySet_spanproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Submodule.isInternal_prime_power_torsion_of_pidproof · cited by 1
- Submodule.torsionBy_le_torsionBy_of_dvdproof · cited by 0
- Submodule.supIndep_torsionByproof · cited by 0
- Submodule.torsionBySet_ideal_span_singleton_eqproof · cited by 0
- Submodule.iSup_torsionBy_eq_torsionBy_prodproof · cited by 0
- Submodule.torsionBy_isInternalproof · cited by 0