Theorems · Definition · commutative algebra
Module.IsTorsionBySet.hasSMul
{R : Type u_1} →
{M : Type u_2} →
[inst : Ring R] →
[inst_1 : AddCommGroup M] → [inst_2 : Module R M] → {I : Ideal R} → Module.IsTorsionBySet R M ↑I → SMul (R ⧸ I) Mcan't be an instance because hM can't be inferred
- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
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.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coestatement and proof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Submodule.toAddSubgroupproof · cited by 106
- Module.IsTorsionBySetstatement and proof · cited by 24
- smulAddHomproof · cited by 17
- QuotientAddGroup.liftproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- Module.IsTorsionBy.hasSMulproof · cited by 1
- Module.IsTorsionBySet.mk_smulstatement · cited by 0