Theorems · Theorem · commutative algebra
IsArtinian.subsingleton_of_injective
∀ {R : Type u_1} {P : Type u_3} {N : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid P] [inst_2 : AddCommMonoid N]
[inst_3 : Module R P] [inst_4 : Module R N] [IsArtinian R N] {f : P × N →ₗ[R] N},
Function.Injective ⇑f → Subsingleton P- Defined in
- Mathlib.RingTheory.Artinian.Module
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, 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
- LinearMap.compproof · cited by 1,642
- IsArtinianstatement and proof · cited by 69
- LinearMap.inrproof · cited by 62
- Prod.mk_right_injectiveproof · cited by 15
- IsArtinian.surjective_of_injective_endomorphismproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- StrongRankCondition.of_isArtinianproof · cited by 0