Just to confirm the accepted answer, I link here relevant definitions from [Springer Online Encyclopaedia of Mathematics](https://encyclopediaofmath.org/wiki/Main_Page) (definitely more reliable source than MathWorld and even PlanetMath...):

[Nilpotent algebra](https://encyclopediaofmath.org/wiki/Nilpotent_algebra)

[Locally nilpotent algebra](https://encyclopediaofmath.org/wiki/Locally_nilpotent_algebra)

[Nil algebra](https://encyclopediaofmath.org/wiki/Nil_algebra)

So the most appropriate thing to say would be "the augmentation ideal is nilpotent". This terminology is very standard.