Theorems · Theorem · commutative algebra
Module.coe_length
∀ (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.krullDim (Submodule R M)
- Defined in
- Mathlib.RingTheory.Length
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 38 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.
Cites10
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
- Submodulestatement and proof · cited by 7,192
- ENatstatement · cited by 4,985
- WithBotstatement · cited by 1,498
- WithBot.somestatement · cited by 541
- Order.krullDimstatement and proof · cited by 82
- Module.lengthstatement · cited by 56
- WithBot.coe_unbotproof · cited by 10
Cited by10
Results whose statement or proof uses this declaration.
- LinearEquiv.length_eqproof · cited by 7
- Module.length_compositionSeriesproof · cited by 4
- Module.length_eq_one_iffproof · cited by 4
- Module.length_quotientproof · cited by 3
- Module.length_submoduleproof · cited by 2
- Module.length_eq_zero_iffproof · cited by 2
- Module.length_eq_heightproof · cited by 1
- Module.length_eq_top_iff_infiniteDimensionalOrderproof · cited by 1
- Module.length_eq_coheightproof · cited by 0
- Submodule.length_le_length_restrictScalarsproof · cited by 0