Theorems · Theorem · commutative algebra
Module.length_quotient
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Submodule R M},
Module.length R (M ⧸ N) = Order.coheight N- Defined in
- Mathlib.RingTheory.Length
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 90 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.
Cites18
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
- Set.Elemproof · cited by 7,166
- ENatstatement and proof · cited by 4,985
- HasQuotient.Quotientstatement and proof · cited by 2,301
- WithBotproof · cited by 1,498
- Set.Iciproof · cited by 1,070
- WithBot.someproof · cited by 541
- Order.krullDimproof · cited by 82
- Order.coheightstatement and proof · cited by 74
Cited by3
Results whose statement or proof uses this declaration.
- IsLocalization.AtPrime.ramificationIdx_map_eq_ramificationIdxproof · cited by 1
- IsDiscreteValuationRing.length_quotient_pow_maximalIdealproof · cited by 1
- Submodule.length_quotient_ltproof · cited by 0