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

Authors: Popa V.

### Abstract

Let $\Cal L$ be the class of locally compact commutative groups. For any $X \in \Cal L,$ let $E(X)$ be the ring of all continuous endomorphisms of $X.$ With respect to the compact-open topology, $E(X)$ is a complete Hausdorff topological ring. In this paper we describe, for certain restricted subclasses $\Cal S$ of $\Cal L,$ the structure of those groups $X \in \Cal S$ for which every element of the topological ring $E(X)$ is either a unit, or a topological idempotent, or a topological nilpotent. We also determine the structure of those groups $X \in \Cal L$ for which every element of $E(X)$ is either a unit, or a topological idempotent, or an algebraic nilpotent.

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