Theorems · Theorem · commutative algebra
isArtinian_of_surjective
∀ {R : Type u_1} (M : Type u_2) {P : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid P]
[inst_3 : Module R M] [inst_4 : Module R P] (f : M →ₗ[R] P),
Function.Surjective ⇑f → ∀ [IsArtinian R M], IsArtinian R P- Defined in
- Mathlib.RingTheory.Artinian.Module
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Submoduleproof · cited by 7,192
- Submodule.comapproof · cited by 347
- IsArtinianstatement and proof · cited by 69
- IsWellFounded.wfproof · cited by 43
- Submodule.comap_strictMono_of_surjectiveproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- isArtinian_of_linearEquivproof · cited by 1
- IsFiniteLength.of_surjectiveproof · cited by 1