Theorems · Theorem · commutative algebra
Module.length_eq_height
∀ (R : Type u_1) (M : Type u_2) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M], Module.length R M = Order.height ⊤
- Defined in
- Mathlib.RingTheory.Length
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 59 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
- Top.topstatement and proof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · 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
- Order.heightstatement and proof · cited by 67
- Module.lengthstatement and proof · cited by 56
- Module.coe_lengthproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Module.length_topproof · cited by 3