Baer modules over domains

Eklof, Paul C.; Fuchs, László; Shelah, Saharon

doi:10.1090/S0002-9947-1990-0974514-8

Baer modules over domains
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by Paul C. Eklof, László Fuchs and Saharon Shelah

Trans. Amer. Math. Soc. 322 (1990), 547-560

DOI: https://doi.org/10.1090/S0002-9947-1990-0974514-8

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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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Baer modules over domains
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Abstract: