IMCS/Publications/BASM/Issues/BASM n.3 (22), 1996/

Units, idempotents and nilpotents of an endomorphism ring. I. (English)

Authors: Popa Mihail


For any locally compact commutative group $X,$ the set $E(X)$ of all continuous endomorphisms of $X$, endowed with the compact-open topology, is a complete Hausdorff topological ring. In this paper we give a necessary condition on $X$ in order that every element of the topological ring $E(X)$ be either a unit, or a topological idempotent, or a topological nilpotent. We also determine the structure of those groups $X$ for which $E(X)$ is a division ring and the structure of those groups $X$ for which every element of $E(X)$ is a topological idempotent.

Institutul de Matematică Academia de Ştiinţe a Moldovei
str. Academiei 5, Chişinău, MD-2028 Moldova