Theorems · Theorem · commutative algebra
isFiniteLength_of_exists_compositionSeries
∀ {R : Type u_1} [inst : Ring R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M],
(∃ s, RelSeries.head s = ⊥ ∧ RelSeries.last s = ⊤) → IsFiniteLength R M- Defined in
- Mathlib.RingTheory.FiniteLength
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 92 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.
Cites31
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
- RingHom.idproof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Set.ofPredstatement and proof · cited by 6,101
- Bot.botstatement and proof · cited by 4,720
- LinearEquivproof · cited by 3,317
- HasQuotient.Quotientproof · cited by 2,301
- LinearEquiv.symmproof · cited by 1,461
- Submodule.mapproof · cited by 614
Cited by3
Results whose statement or proof uses this declaration.
- isFiniteLength_iff_isNoetherian_isArtinianproof · cited by 14
- isFiniteLength_iff_exists_compositionSeriesproof · cited by 4
- Module.length_compositionSeriesproof · cited by 4