9 problems

Medvedev's conjecture. $L$ contains a solvable subring of $m$-bounded derived length whose index is $(p,n,m)$-bounded.

A Lie algebra is semisimple if it has no nonzero solvable ideals, and an iUA-Lie ring is a Lie ring for which every commutator-preserving injection into another Lie ring is additiv…

Let $\mathfrak{g}$ be an infinite simple Lie ring of finite Morley rank, and suppose that its characteristic is sufficiently large. Cherlin–Zilber conjecture for Lie rings. Then…

Let $T$ be a finite-dimensional theory, meaning that it carries a dimension function on interpretable sets satisfying the usual invariance, finiteness, union, and fiber-dimension a…

A definable simple Lie ring of finite Morley rank is a Lie ring $\mathfrak{g}$ definable in a structure of finite Morley rank. Its characteristic is the characteristic associated w…

Let $\mathfrak{g}$ be an infinite simple Lie ring of finite Morley rank. Assume that its characteristic is sufficiently large. Large-characteristic conjecture. Then $\mathfrak{g}$…

For each $c\in\mathbb{N}$, let $\mathfrak{f}_{c,2}$ be the free class-$c$ nilpotent Lie ring on two generators, and let…

Let $\mathfrak{f}_{c,d}$ denote the free class-$c$ nilpotent Lie rings on $d$ generators defined over $\mathbb{Z}$. For $c,d\in\mathbb{N}$, let…

Let $\mathcal{L}$ be a graded Lie lattice. A grading is a decomposition of the underlying free $\mathbb{Z}$-module compatible with the Lie bracket, and its weight is the correspond…