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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Baer modules over domains

Authors: Paul C. Eklof, László Fuchs and Saharon Shelah
Journal: Trans. Amer. Math. Soc. 322 (1990), 547-560
MSC: Primary 13C13; Secondary 13C10, 13F05
MathSciNet review: 974514
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Abstract: For a commutative domain $ R$ with $ 1$, an $ R$-module $ B$ is called a Baer module if $ \operatorname{Ext} _R^1(B,T) = 0$ for all torsion $ R$-modules $ T$. The structure of Baer modules over arbitrary domains is investigated, and the problem is reduced to the case of countably generated Baer modules. This requires a general version of the singular compactness theorem. As an application we show that over $ h$-local Prüfer domains, Baer modules are necessarily projective. In addition, we establish an independence result for a weaker version of Baer modules.

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Keywords: Baer module, flat and projective modules, continuous ascending chains, Prüfer domains, constructibility, Proper Forcing Axiom, singular compactness
Article copyright: © Copyright 1990 American Mathematical Society