## On regular endomorphism rings of topological Abelian groups.(English)Zbl 1240.20055

Summary: We extend a result of Rangaswamy about regularity of endomorphism rings of Abelian groups to arbitrary topological Abelian groups. Regularity of discrete quasi-injective modules over compact rings modulo radical is proved. A characterization of torsion LCA groups $$A$$ for which $$\mathrm{End}_c(A)$$ is regular is given.

### MSC:

 20K45 Topological methods for abelian groups 22B05 General properties and structure of LCA groups 16S50 Endomorphism rings; matrix rings 20K30 Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups 16W80 Topological and ordered rings and modules 16E50 von Neumann regular rings and generalizations (associative algebraic aspects)
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### References:

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