Theorems · Theorem · commutative algebra

Module.Projective.of_split

∀ {R : Type u_1} [inst : Semiring R] {P : Type u_2} [inst_1 : AddCommMonoid P] [inst_2 : Module R P] {M : Type u_3}
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [Module.Projective R M] (i : P →ₗ[R] M) (s : M →ₗ[R] P),
  s ∘ₗ i = LinearMap.id → Module.Projective R P

A direct summand of a projective module is projective.

Defined in

Mathlib.Algebra.Module.Projective

Cited by

7 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleAddCommMonoidModuleModule.Projective