Soluble Lie rings of finite Morley rank

Abstract

We do two things. 1. As a corollary to a stronger linearisation result (Theorem A), we prove the finite Morley rank version of the Lie-Kolchin-Malcev theorem on Lie algebras (Corollary A2). 2. We classify Lie ring actions on modules of characteristic not 2, 3 and Morley rank 2 (Theorem B).