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Theorems · Theorem · commutative algebra

Submodule.torsionBy_isTorsionBy

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

The a-torsion submodule is an a-torsion module.

Defined in
Mathlib.Algebra.Module.Torsion.Basic
Cited by
1 results in Mathlib
Foundations
Depth 28 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.

Submodule.torsionBy_torsionBy_eq_top · cited by 0Submodule.torsionBy_torsi…Module · cited by 20661ModuleAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringSubmodule · cited by 7192SubmoduleSubmodule.torsionBy · cited by 31Submodule.torsionByModule.IsTorsionBy · cited by 15Module.IsTorsionBySubmodule.smul_torsionBy · cited by 4Submodule.smul_torsionBySubmodule.torsionBy_isTorsion…CITED BYCITES

Cites7

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Cited by1

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