Theorems · Theorem · commutative algebra
Module.length_eq_zero_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 = 0 ↔ Subsingleton M- Defined in
- Mathlib.RingTheory.Length
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 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.
Cites14
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
- Ringstatement and proof · cited by 7,463
- Submoduleproof · cited by 7,192
- ENatstatement and proof · cited by 4,985
- WithBotproof · cited by 1,498
- WithBot.someproof · cited by 541
- Order.krullDimproof · cited by 82
- Module.lengthstatement · cited by 56
- WithBot.coe_injproof · cited by 18
- WithBot.coe_zeroproof · cited by 10
- Module.coe_lengthproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- Module.length_eq_zeroproof · cited by 9
- Module.length_pos_iffproof · cited by 2