Algebraic commutators with respect to subnormal subgroups in division rings

Let $$D$$ be a division ring and $$K$$ subfield of which is not necessarily contained in the center $$F$$ . We study structure under condition left algebraicity certain subsets over Among others, it proved that if $$D^*$$ contains noncentral normal subgroup algebraic bounded degree $$d$$ , then $$[D:F]\le d^2$$ In case $$K=F$$ obtained results show either all additive commutators or multiplicative with respect to subnormal are $$f$$