nilpotent ideal

For $n$ a positive integer and $I$ a (left) ideal of a ring $R$, let $I^n$ denote the ideal of $R$ consisting of all finite sums of $n$-tuple products $i_1\cdots i_n$ of elements in $I$.

A (left) ideal $I$ of a ring $R$ is **nilpotent** if there exists a positive natural number $n$ such that $I^n$ is the zero ideal of $R$.