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On regular endomorphism rings of topological Abelian groups

Horea Florian Abrudan (2011)

Czechoslovak Mathematical Journal

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 End c ( A ) is regular is given.

On residually finite groups and their generalizations

Andrzej Strojnowski (1999)

Colloquium Mathematicae

The paper is concerned with the class of groups satisfying the finite embedding (FE) property. This is a generalization of residually finite groups. In [2] it was asked whether there exist FE-groups which are not residually finite. Here we present such examples. To do this, we construct a family of three-generator soluble FE-groups with torsion-free abelian factors. We study necessary and sufficient conditions for groups from this class to be residually finite. This answers the questions asked in...

On resolvable spaces and groups

Luis Miguel Villegas-Silva (1995)

Commentationes Mathematicae Universitatis Carolinae

It is proved that every uncountable ω -bounded group and every homogeneous space containing a convergent sequence are resolvable. We find some conditions for a topological group topology to be irresolvable and maximal.

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