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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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