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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 the nontrivial solvability of systems of homogeneous linear equations over in ZFC

Jan Šaroch (2020)

Commentationes Mathematicae Universitatis Carolinae

Motivated by the paper by H. Herrlich, E. Tachtsis (2017) we investigate in ZFC the following compactness question: for which uncountable cardinals κ , an arbitrary nonempty system S of homogeneous -linear equations is nontrivially solvable in provided that each of its subsystems of cardinality less than κ is nontrivially solvable in ?

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