arXiv subjects
Publications and source records attributed to Jules Tindzogho Ntsiri.
We prove that NIP nilrings of bounded nilexponent are nilpotent. We also deduce that NIP $ω$-categorical $n$-Engel Lie algebras of characteristic $p>n$ are nilpotent, yielding a case of the Lie algebra analogous of Wilson conjecture for $ω$-categorical groups.
We prove the existence of Cartan subrings, i.e., self-normalizing nilpotent subrings in soluble ranked Lie rings.
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).
We prove the Lie ring equivalent of the Cherlin-Zilber conjecture -- in characteristic 0, for any rank and -- in characteristic not 2, 3 for rank less than or equal to 4. Both are open in the group case.