Engel algebra

An associative algebra or Lie algebra $\mathfrak{g}$ satisfying the Engel condition: For every $X \in \mathfrak{g}$ the inner derivation $\mathrm{ad}\,X$ (cf. Derivation in a ring) is nilpotent. In other words, all elements of an Engel algebra are Engel elements, see also Lie algebra, nil).