Theorems · Theorem · commutative algebra
Module.isTorsionBySet_quotient_set_smul
∀ {R : Type u_1} (M : Type u_2) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (s : Set R),
Module.IsTorsionBySet R (M ⧸ s • ⊤) s- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
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Cites12
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
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- HasQuotient.Quotientstatement · cited by 2,301
- Submodule.mem_topproof · cited by 58
- Submodule.pointwiseSetSMulstatement · cited by 30
- Module.IsTorsionBySetstatement · cited by 24
- Submodule.mem_set_smul_of_mem_memproof · cited by 9
- Module.isTorsionBySet_quotient_iffproof · cited by 4
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