I am interested in a ring $R$ with an ideal $I\subset R$ and the following properties: 1) $R$ is complete with respect to $I$-adic topology; 2) $\cap_{n\geq 1} I^n=\{0\}$; 3) $R/I$ is finite. In particular, I am interested in the case when $I$ is principal.
Is there classification/description/characterization of such rings and ideals?