## Strong Nilpotence and the Jacobson Radical

In the previous post we saw the following definition for a ring $R$: An element $r\in R$ is called strongly nilpotent if every sequence $r = r_0,r_1,r_2,\dots$ such that $r_{n+1}\in r_nRr_n$ is eventually zero. Why introduce this notion? Well, did you know that every finite integral domain is a field? If $R$ is an integral […]