Every factor belongs to exactly one of the following classes:
paragraph
admin
\begin{align*}
I_n,\quad I_\infty,\quad II_1,\quad II_\infty,\quad III.
\end{align*}
latex_env
admin
The distinction is determined by the existence of minimal projections, the finiteness of the identity, and the existence of a faithful normal semifinite trace.