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Theorems · Theorem · commutative algebra

Submodule.torsion_isTorsion

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
  Module.IsTorsion R ↥(Submodule.torsion R M)

The torsion submodule is always a torsion module.

Defined in
Mathlib.Algebra.Module.Torsion.Basic
Cited by
1 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringAddCommMonoidModule
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Module.equiv_free_prod_directSum · cited by 2Module.equiv_free_prod_di…Module · cited by 20661ModuleAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringSubmodule · cited by 7192SubmodulenonZeroDivisors · cited by 895nonZeroDivisorsModule.IsTorsion · cited by 23Module.IsTorsionSubmodule.torsion · cited by 15Submodule.torsionSubmodule.torsion'_isTorsion' · cited by 2Submodule.torsion'_isTors…Submodule.torsion_isTorsionCITED BYCITES

Cites8

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Cited by1

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