nLab nilpotent ideal

Not to be confused with nilradical, the ideal of nilpotent elements.

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Definition

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 $I$.

Definition

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 $R$.

Related concepts

• infinitesimal extension