The Cherlin–Zilber conjecture for definable simple Lie rings

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 with its underlying definable field when such a field is interpretable. Cherlin–Zilber conjecture for Lie rings. Let $\mathfrak{g}$ be a definable simple Lie ring of finite Morley rank. If the characteristic of $\mathfrak{g}$ is sufficiently large, then $\mathfrak{g}$ is a Lie algebra of finite dimension over an algebraically closed field. The paper states that this conjecture has been verified in characteristic $0$, so the remaining scope concerns sufficiently large positive characteristic.