A solution to the Baer splitting problem

Let R R be a commutative domain. We prove that an R R -module B B is projective if and only if E x t R 1 ( B , T ) = 0 \mathrm {Ext}_R^1(B,T)=0 for any torsion module T T . This answers in the affirmative a question raised by Kaplansky in 1962.