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Torsion-free abelian groups with prescribed finitely topologized endomorphism rings

Authors: Manfred Dugas and Rüdiger Göbel
Journal: Proc. Amer. Math. Soc. 90 (1984), 519-527
MSC: Primary 20K20; Secondary 20K30
MathSciNet review: 733399
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Abstract: We will show that any complete Hausdorff ring $ R$ which admits, as a basis of neighborhoods of 0, a family of right ideals $ I$ with $ R/I$ cotorsion-free can be realized as a topological endomorphism ring of some torsion-free abelian group with the finite topology. This theorem answers a question of A. L. S. Corner (1967) and can be used to provide examples in order to solve a problem (No. 72) in L. Fuchs' book on abelian groups.

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Keywords: Torsion-free abelian groups, topological endomorphism ring
Article copyright: © Copyright 1984 American Mathematical Society