A Jordan canonical form for nilpotent elements in an arbitrary ring.

Abstract

In this paper we give an inductive new proof of the Jordan canonical form of a nilpotent element in an arbitrary ring. If is a nilpotent element of index n with von Neumann regular , we decompose with a Jordan block of size n over a corner S of R, and nilpotent of index <n for an idempotent e of R commuting with a. This result makes it possible to characterize prime rings of bounded index n with a nilpotent element of index n and von Neumann regular as a matrix ring over a unital domain.