Regularity conjecture for Jordan-Lie inner ideals of simple locally finite associative algebras

Let $A$ be a simple locally finite associative algebra over $\mathbb{F}$, let $L=[A,A]$, and let $B$ be a Jordan-Lie inner ideal of $L$. Regularity conjecture. Every Jordan-Lie inner ideal $B$ of $L$ is regular. The conjecture proposes that the regularity results established for finite-dimensional associative algebras extend to simple locally finite associative algebras; its general validity remains open.