RT Journal Article T1 A Jordan canonical form for nilpotent elements in an arbitrary ring. A1 García-González, Esther A1 Gómez-Lozano, Miguel Ángel A1 Muñoz-Alcázar, Rubén José A1 Vera de Salas, Guillermo K1 Grupos nilpotentes K1 Anillos (Álgebra) AB 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