Abstract
We construct a pure subgroupG of the Baer-Specker group ℤω with a “small” endomorphism ring giving a split realization of ℤ, in the sense that EndG=⊕ ℤ FinG with |FinG| ≤ 2ℕo, where FinG denotes the ideal of all endomorphisms ofG of finite rank, while its dualG*=Hom (G, ℤ) is as large as possible, i.e. of cardinal 2ℕo. Our groupG gives a complete answer to a question of Irwin (1993). Note that a recent paper [3] answered Irwin’s question under the assumption of the continuum hypothesis CH.
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Dedicated to Georg Nöbeling on the occasion of his 90th birthday on 12th November, 1997.
Partially supported by the Graduierten KollegTheoretische und experimentelle Methoden der reinen Mathematik of Essen University, and a project No. G-0294-081.06/93 of theGerman-Israeli Foundation for Scientific Research & Development
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Corner, A.L.S., Göbel, R. Essentially rigid floppy subgroups of the baer-specker group. Manuscripta Math 94, 319–326 (1997). https://doi.org/10.1007/BF02677856
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DOI: https://doi.org/10.1007/BF02677856