On an analogue of Schur's theorem for Leibniz $n$-algebras

In this paper, we investigate relationships between certain important subalgebras of Leibniz $n$-algebras. In particular, we establish a close connection between the central factor-algebra of a Leibniz $n$-algebra and its derived ideal. As an application, we prove an analogue of the classical group-theoretic Schur's theorem for Leibniz $n$-algebras. The obtained results continue a long line of research on Schur-type theorems in various algebraic structures and generalize known related results from the theories of Leibniz algebras and Lie algebras.