# Contents

## 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 $R$.

Revised on July 10, 2015 13:17:19 by Ingo Blechschmidt (137.250.162.16)