Fully noncentral Lie ideals and invariant additive subgroups in rings
Fully noncentral Lie ideals and invariant additive subgroups in rings
We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully noncentral, that is, its image in every quotient is noncentral. For a unital algebra over a field of characteristic $\neq 2$ …