Weyl's theorem states that finite-dimensional representations of finite dimensional semisimple Lie algebras are completely reducible (expressible as a direct sum of irreducible submodules), with some sources stating a requirement for algebraic closure, some for characteristic $0$, and some for neither.
What is necessary? Many proofs I've seen use Schur's lemma (irreducible module homomorphisms are scalar multiplication) without stipulating the need for algebraic closure, which I thought was a requirement.