As for any topological ring, one can ask whether is complete (as a uniform space); if it is not, one considers its completion, again a local ring. Complete Noetherian local rings are classified by the Cohen structure theorem.
As for any topological ring, one can, ask whether is complete (as a uniform space); if it is not, one considers its completion again a local ring. Complete Noetherian local rings are classified by the Cohen structure theorem.