Just to confirm the accepted answer, I link here relevant definitions from <a href="http://eom.springer.de/">Springer Online Encyclopaedia of Mathematics</a> (definitely more reliable source than MathWorld and even PlanetMath...): <a href="http://eom.springer.de/n/n066700.htm">Nilpotent algebra</a> <a href="http://eom.springer.de/l/l060470.htm">Locally nilpotent algebra</a> <a href="http://eom.springer.de/n/n066640.htm">Nil algebra</a> So the most appropriate thing to say would be "the augmentation ideal is nilpotent". This terminology is very standard.