Lecture Notes on Bayesian Estimation and Classification
《Lecture Notes on Bayesian Estimation and Classification》 · 第 127 页 · Chapter 5，Section 5.1「Abelian and Central Series」，小节「Triangular and Unitriangular Groups」
Let $S$ be a ring with identity and let $N$ be a subring of $S$. Write $N^{(i)}$ for the set of all sums of products of $i$ elements of $N$ where $i>0$; clearly $N^{(i)}$ is a subring. Also $N^{(i)}=0$ if and only if all products of $i$ elements of $N$ vanish. If some $N^{(i)}$ equals $0$, then $N$ is said to be nilpotent.