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Units, idempotents and nilpotents of an endomorphism ring. I. (English)
Authors: Popa Mihail
Abstract
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
str. Academiei 5, Chişinău, MD-2028 Moldova
Contents
- Vasilii Grigorievich Cheban. A tribute in honor of his 80th birthday.
- On the stability of effective solutions of a vector trajectory problem of discrete optimization. I. (Russian)
- Topological rings whose subrings are linearly compact. (English)
- The group of units of a locally compact ring. (English)
- Independence and quasiregularity in algebras. I. (Romanian)
- Acceleration of the solution of the problem of the natural oscillations of a body by the finite element method. (Russian)
- Paracompact extentions and orderability of spaces. (English)
- Typical representation of polynomial differential systems by means of first-order comitants. (Russian)
- On equation of geodesic deviation and its solutions. (English)
- A network transportation problem with concave cost functions of the flow on network edges, and its applications. (Russian)
- Units, idempotents and nilpotents of an endomorphism ring. I. (English)
- Foundations of the general theory of $W\sb q$-symmetry. (Russian)
- $L\sb p$-theory of generalized solutions of linear parabolic conjugation problems. (Russian)
- The repartition of multiplicity between three real isp of cubis differential system. (English)
- On the nilpotency of finitely determined nil algebras. (English)
