Theorems · Definition · commutative algebra
Module.IsTorsion
(R : Type u_1) → (M : Type u_2) → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [Module R M] → Prop
A torsion module is a module where every element is a-torsion for some non-zero-divisor a.
- Defined in
- Mathlib.Algebra.Module.Torsion.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- nonZeroDivisorsproof · cited by 895
Cited by23
Results whose statement or proof uses this declaration.
- Module.equiv_directSum_of_isTorsionstatement and proof · cited by 2
- Submodule.isInternal_prime_power_torsionstatement and proof · cited by 2
- Module.rank_eq_zero_iff_isTorsionstatement · cited by 2
- isAddTorsion_iff_isTorsion_intstatement and proof · cited by 2
- Submodule.isInternal_prime_power_torsion_of_pidstatement and proof · cited by 1
- Ideal.iSup_primaryComponent_eq_topstatement and proof · cited by 1
- Module.AEval.isTorsion_of_aeval_eq_zerostatement · cited by 1
- Submodule.exists_isInternal_prime_power_torsion_of_pidstatement and proof · cited by 1
- Submodule.torsion_isTorsionstatement · cited by 1
- Module.IsTorsion.rank_eq_zerostatement and proof · cited by 1
- Submodule.annihilator_top_inter_nonZeroDivisorsstatement and proof · cited by 1
- Module.finite_of_fg_torsionstatement and proof · cited by 1