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Soluble Lie rings of finite Morley rank

Adrien Deloro and Jules Tindzogho Ntsiri
Vol. 4 (2025), No. 2, 163–175
DOI: 10.2140/mt.2025.4.163
Abstract

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). We also classify Lie ring actions on modules of characteristic ≠2,3 and Morley rank 2 (Theorem B).

Keywords
Lie rings, Morley rank, model-theoretic algebra
Mathematical Subject Classification
Primary: 03C60, 17B50
Secondary: 20F11
Milestones
Received: 8 October 2024
Revised: 23 March 2025
Accepted: 24 March 2025
Published: 11 April 2025
Authors
Adrien Deloro
Sorbonne Université
Université Paris Cité
CNRS, IMJ-PRG
F-75005 Paris
France
Jules Tindzogho Ntsiri
Department of Mathematics and Informatics, Faculty of Sciences
Masuku University of Science and Technology (USTM)
Franceville
Gabon
© 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers).