  The aim of this article is to obtain variations on the classical theorems of
Schur and Baer on finiteness of commutator subgroups, valid in the contexts of
Lie algebras and Leibniz algebras over a field. Using non-abelian tensor
products and exterior products, we prove Schur's Theorem for finitely generated
Leibniz algebras, both Schur's Theorem and Baer's Theorem for finitely
generated Lie algebras, and a version of these theorems for finitely presented
Lie algebras.
