Theorems · Inductive type · commutative algebra
IsFiniteLength
(R : Type u_1) → [inst : Ring R] → (M : Type u_2) → [inst_1 : AddCommGroup M] → [Module R M] → Prop
A module of finite length is either trivial or a simple extension of a module known to be of finite length.
- Defined in
- Mathlib.RingTheory.FiniteLength
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- RingAddCommGroupModule
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 · cited by 20,661
- AddCommGroupstatement · cited by 12,871
- Ringstatement · cited by 7,463
Cited by24
Results whose statement or proof uses this declaration.
- isFiniteLength_iff_isNoetherian_isArtinianstatement and proof · cited by 14
- Module.length_ne_top_iffstatement and proof · cited by 8
- Module.length_eq_add_of_exactproof · cited by 6
- Module.length_compositionSeriesproof · cited by 4
- isFiniteLength_iff_exists_compositionSeriesstatement and proof · cited by 4
- isFiniteLength_of_exists_compositionSeriesstatement and proof · cited by 3
- IsArtinianRing.tfaestatement · cited by 2
- IsSemiprimaryRing.isNoetherian_iff_isArtinianproof · cited by 2
- IsSemisimpleModule.finite_tfaestatement · cited by 2
- Module.finite_iff_isArtinianRingproof · cited by 2
- LinearEquiv.isFiniteLengthstatement and proof · cited by 1
- IsSemiprimaryRing.isNoetherian_iff_finite_of_jacobson_fgproof · cited by 1