nilpotent ideal

Let \(A\) be a ring and \(\mathfrak{a} \subseteq A\) an ideal . Then \(\mathfrak{a}\) is said to be nilpotent, if there exists an $n ∈ \(\mathbb{N}\) such that

\begin{align*} \mathfrak{a}^n = 0 \end{align*}

see: product of ideals