Theorems · Theorem · commutative algebra
Module.length_le_of_injective
∀ {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] (f : N →ₗ[R] M),
Function.Injective ⇑f → Module.length R N ≤ Module.length R M- Defined in
- Mathlib.RingTheory.Length
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Ringstatement and proof · cited by 7,463
- ENatstatement and proof · cited by 4,985
- LinearMap.rangeproof · cited by 893
- Submodule.mkQproof · cited by 232
- le_self_addproof · cited by 68
- Module.lengthstatement and proof · cited by 56
- Submodule.mkQ_surjectiveproof · cited by 48
Cited by3
Results whose statement or proof uses this declaration.
- Module.length_finsuppproof · cited by 2
- Module.length_piproof · cited by 0
- Ring.ord_zeroproof · cited by 0