I'd like a name for an augmented algebra $A = \langle 1\rangle \oplus A_+$ for which there is an $N$ so that any product of more than $N$ elements in the augmentation ideal is $0$, i.e., $(A_+)^N = 0$.  Is there a name?  It seems related to nilpotence, and it implies that all elements in $A_+$ are nilpotent, but is stronger than that.  There is a uniform bound on the degree of nilpotence, but that's not enough either, as the example of the exterior algebra in infinitely many variables over $\mathbb{Z}/2$ shows.

MathWorld defines a nilpotent algebra or nilalgebra to be one where every element is nilpotent.  (They are therefore not considering unital algebras, contrary to an [earlier discussion][1] here.)  Is this standard?  Is there a better term?


  [1]: https://mathoverflow.net/questions/15107/algebra-unital-associative-algebra-better-terminology