Theorems · Theorem · commutative algebra
LinearEquiv.length_eq
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Type u_3}
[inst_3 : AddCommGroup N] [inst_4 : Module R N] (e : M ≃ₗ[R] N), Module.length R M = Module.length R N- Defined in
- Mathlib.RingTheory.Length
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- RingHom.idstatement and proof · cited by 18,349
- 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
- LinearEquivstatement and proof · cited by 3,317
- WithBotproof · cited by 1,498
- WithBot.someproof · cited by 541
- Order.krullDimproof · cited by 82
- Module.lengthstatement and proof · cited by 56
- Submodule.orderIsoMapComapproof · cited by 16
Cited by7
Results whose statement or proof uses this declaration.
- Module.length_of_freeproof · cited by 3
- Ideal.ramificationIdx_tower'proof · cited by 2
- Module.length_finsuppproof · cited by 2
- Ideal.ramificationIdx_smulproof · cited by 2
- Module.length_pi_of_fintypeproof · cited by 2
- CovBy.length_baseChangeproof · cited by 1
- Ideal.sum_ramification_inertia_eq_finrank_fiberproof · cited by 1