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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Torsion-free abelian groups with prescribed finitely topologized endomorphism rings
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by Manfred Dugas and Rüdiger Göbel PDF
Proc. Amer. Math. Soc. 90 (1984), 519-527 Request permission

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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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 519-527
  • MSC: Primary 20K20; Secondary 20K30
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0733399-8
  • MathSciNet review: 733399