Theorems · Theorem · commutative algebra
Module.length_ne_top_iff
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M],
Module.length R M ≠ ⊤ ↔ IsFiniteLength R M- Defined in
- Mathlib.RingTheory.Length
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 95 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.
Cites23
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
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submoduleproof · cited by 7,192
- Set.ofPredproof · cited by 6,101
- ENatstatement and proof · cited by 4,985
- Bot.botproof · cited by 4,720
- SetRelproof · cited by 581
- RelSeries.lengthproof · cited by 195
- RelSeries.lastproof · cited by 114
- RelSeries.headproof · cited by 89
Cited by8
Results whose statement or proof uses this declaration.
- Module.length_eq_add_of_exactproof · cited by 6
- Ideal.ramificationIdx_posproof · cited by 5
- Ring.ord_eq_addValproof · cited by 3
- Module.length_of_freeproof · cited by 3
- IsLocalRing.length_baseChangeproof · cited by 1
- IsLocalRing.length_restrictScalarsproof · cited by 1
- Module.length_ne_topproof · cited by 1
- Module.finiteDimensionalOrder_submodule_iffproof · cited by 0