Theorems · Theorem · commutative algebra

Module.Finite.exists_comp_eq_id_of_projective

∀ (R : Type u_1) (M : Type u_2) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [Module.Finite R M]
  [Module.Projective R M], ∃ n f g, Function.Surjective ⇑f ∧ Function.Injective ⇑g ∧ f ∘ₗ g = LinearMap.id

Defined in: Mathlib.RingTheory.Finiteness.Projective
Cited by: 3 results in Mathlib
Foundations: Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Semiring AddCommMonoid Module Module.Finite Module.Projective

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Cites13

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.compstatement and proof · cited by 1,642
Module.Finitestatement and proof · cited by 1,032
LinearMap.idstatement and proof · cited by 625
Module.Projectivestatement and proof · cited by 82
Module.projective_lifting_propertyproof · cited by 13
Module.Finite.exists_fin'proof · cited by 10

Cited by3

Results whose statement or proof uses this declaration.

dualTensorHom_bijectiveproof · cited by 6
Module.finitePresentation_of_projectiveproof · cited by 2
dualTensorHom_bijective_of_finite_projective_rightproof · cited by 0