Theorems · Theorem · linear algebra
Module.End.injective_of_surjective
∀ (R : Type u_1) (M : Type u_2) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Module.Free R M]
[Module.Finite R M] [IsStablyFiniteRing R] {f : Module.End R M}, Function.Surjective ⇑f → Function.Injective ⇑f- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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
- LinearMapproof · cited by 10,215
- LinearMap.compproof · cited by 1,642
- Module.Finitestatement and proof · cited by 1,032
- Module.Endstatement and proof · cited by 774
- LinearMap.idproof · cited by 625
- Module.Freestatement and proof · cited by 597
- Module.projective_lifting_propertyproof · cited by 13
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