Theorems · Definition · commutative algebra
Module.IsTorsionBy
(R : Type u_1) → (M : Type u_2) → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [Module R M] → R → Prop
An a-torsion module is a module where every element is a-torsion.
- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
Cited by17
Results whose statement or proof uses this declaration.
- Module.isTorsionBySet_singleton_iffstatement and proof · cited by 3
- Module.isTorsionBy_iff_torsionBy_eq_topstatement and proof · cited by 2
- Module.isTorsionBy_quotient_iffstatement · cited by 2
- Module.isTorsionBySet_span_singleton_iffstatement · cited by 1
- Submodule.torsionBy_isTorsionBystatement · cited by 1
- Module.exists_smul_eq_zero_and_mk_eqstatement and proof · cited by 1
- Submodule.exists_isTorsionBystatement · cited by 1
- Module.IsTorsionBy.hasSMulstatement and proof · cited by 1
- Module.p_pow_smul_liftstatement and proof · cited by 1
- Module.torsion_by_prime_power_decompositionproof · cited by 1
- Module.isTorsionBy_iff_mem_annihilatorstatement · cited by 0
- Module.isTorsionBy_iff_mem_ker_lsmulstatement · cited by 0