Baer Modules over Domains

For a commutative domain with , an -module is called a Baer module if <!-- MATH $\operatorname{Ext} _R^1(B,T) = 0$ --> for all torsion -modules . 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 -local Prüfer domains, Baer modules are necessarily projective. In addition, we establish an independence result for a weaker version of Baer modules.