Baer modules over domains

Abstract

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