Theorems · Theorem · commutative algebra
Module.length_eq_of_surjective
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {S : Type u_3}
[inst_3 : CommRing S] [inst_4 : Algebra S R] [inst_5 : Module S M] [IsScalarTower S R M],
Function.Surjective ⇑(algebraMap S R) → Module.length S M = Module.length R M- Defined in
- Mathlib.RingTheory.Length
- Cited by
- 4 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.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- LinearMapproof · cited by 10,215
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Submoduleproof · cited by 7,192
- ENatstatement and proof · cited by 4,985
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.ramificationIdx_posproof · cited by 5
- Ideal.ramificationIdx_smulproof · cited by 2
- Ideal.sum_ramification_inertia_eq_finrank_fiberproof · cited by 1
- CovBy.length_restrictScalarsproof · cited by 1