View source for Engel algebra

An associative algebra or Lie algebra <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035670/e0356701.png" /> satisfying the Engel condition: For every <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035670/e0356702.png" /> the inner derivation <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035670/e0356703.png" /> (cf. [[Derivation in a ring|Derivation in a ring]]) is nilpotent. In other words, all elements of an Engel algebra are Engel elements (cf. [[Engel element|Engel element]], see also [[Lie algebra, nil|Lie algebra, nil]]).